In this post, I assess Craig's metaethical argument by means of a hypothetical debate between Bob - a defender of Craig's metaethical argument[a], and of Craig's version of Divine Command Theory (henceforth, DCT) – and Alice – a non-theist who believes that the second premise of Craig's argument is true.
Alice also believes that the argument from moral evil – at least, in its evidential version, if there is a significant difference between the logical and evidential versions – is a decisive argument against the existence of an omnipotent, omniscient, morally perfect (henceforth, omnimax) being – though she holds that there are other, independent and also decisive arguments.
Still, the debate below is not about the argument from moral evil, but mostly about DCT and potential non-theistic accounts, and Craig's first premise.
Before I go on, I would like to clarify that:
1. I don't claim that Craig holds all of the views defended by Bob. Bob is a fictional character, as is Alice. When I attribute views to Craig, I will make that clear, providing relevant links and/or references if needed (e. g., I won't provide a reference or link if I say Craig claims that God exists because it's obvious that he does, but I will if I say he makes a specific claim about the concept of God).
2. I don't claim that any of the views in the post are original.
2. The hypothetical debate.
Alice: No omnimax being exists. There are several ways to see that, but – for example -, an omnimax being would not create a universe with so much suffering, or with moral agents with an imperfect moral sense. They would have flawless moral knowledge.
Moreover, she would prevent at least many of the instances of moral evil that actually occur – well, actually, she wouldn't need to intervene because she would not create beings inclined to do such evil in the first place, but in any event, if such beings existed even if not created by her, she just wouldn't allow that.
Bob: You're mistaken. God exists. And he is the greatest conceivable being, so in particular, he is an omnimax being. In fact, the very existence of moral evil shows that God exists.
There is a very clear argument, defended by Craig:
P1: If God did not exist, then objective moral values and duties would not exist. 
P2: Objective moral values and duties do exist.
C: God exists.
Alice: I'm familiar with Craig's argument, and I agree that P2 is true, but I see no good reason to think P1 is true. Why do you believe P1?
Bob: Only theism can provide an ontological grounding of moral goodness and/or of moral obligations – as Craig's DCT does -, in the sense of informative identification.
For example, moral goodness are identified with resemblance to some qualities of God, whereas moral obligations are identified with God's commands.
This is akin to the way in which, say, water is identified with H2O, heat with molecular motion, or – to use Craig's own example – the way in which a meter – in the past – was identified with the distance between two lines on a bar in Paris. 
Bob: By 'God' I mean what Craig means, i. e., the greatest conceivable being. In particular, given that moral goodness is a great-making property, God is morally perfect  and that entails he is maximally morally good.
Alice: Okay, so I will grant the water and heat identifications for the sake of the argument, but let me point out that not having an informative identification account is not a problem (see, for example, this post).
That aside, the account given by DCT, as you describe it, is not only not informative, but it seems to be circular.
In fact, the account identifies moral goodness with resemblance to God in some respects, defines the word 'God' as 'the greatest conceivable being', and uses 'great' in a way such that 'God is morally good' is a conceptual truth, and moreover, moral goodness is a great-making property.
As Craig says, asking why God is good is like asking why bachelors are unmarried. But then, identifying moral goodness with resemblance to God seems akin to identifying being unmarried with resemblance to being who – by definition – is a bachelor and has such-and-such properties.
Bob: 'God' is defined in terms of greatness, not in terms of moral goodness, and it seems to me that a proper informative account of bachelorhood would identify being a bachelor with being unmarried and having such-and-such properties.
Alice: But that goes in the other direction. DCT seems similar not to an identification of bachelorhood in terms of unmarriedness – plus some other properties -, but to an identification of unmarriedness in terms of bachelorhood, or more precisely, in terms of resemblance to a certain bachelor. That seems viciously circular.
Bob: I disagree. I see no circularity problem. I don't know what you're getting at.
Alice: Okay, let's me raise the circularity issue from a different perspective. I would ask you what greatness is – that is, I'm asking for the ontological foundation of greatness, in the sense of informative identification.
If you reply that greatness is resemblance to God in some respects, and you define 'God' as 'the greatest conceivable being', then there is a circularity problem. Moreover, moral goodness is a great-making property. So, it seems that to be great is to be morally good and to have such-and-such properties (for some 'such-and-such'). But according to DCT, to be morally good is to resemble the maximally great being.
Do you see the problem?
To be great is to be morally good and to have such-and-such properties, and to be morally good is to resemble the greatest conceivable being. That seems circular.
Bob: You misunderstand the account. There is no circularity. For example, one might stipulate – as it was in the past – that to be a meter long is to be as long as the distance between two lines on a certain standard bar.
If someone were to then ask what it is to be a meter long, it would be informative to tell him that to be a meter long is to be as long as the distance between two lines on the bar in question.
That is informative. The bar itself – or more precisely, the part of the bar between the two lines - has the property of being a meter long, and indeed it is the paradigm of a meter.
Similarly, God has the property of being morally good – indeed, to a maximal degree -, but also God is the paradigm of moral goodness, and that is not problematic. The account of moral goodness provided by DCT is informative.
Alice: Let's say 'meter' is defined as the distance between the lines in question, as it once was.
If someone asks what a meter is, it is proper and informative to tell her that to be a meter long is to be as long as the distance between the lines on that bar, over there, in Paris., and/or that a meter is a distance equal to the distance between the lines on that bar, over there, in Paris., etc.
On the other hand, it would be improper, circular, and not informative to tell her that to be a meter long is to be as long as the distance between two lines that are at a distance of one meter, or that to be a meter long is to be as long as the distance between the lines on a bar that has two lines at a distance of one meter. That's what DCT looks like, as you described it.
Do you see the problem?
Bob: I see, and know I understand in which way you misunderstand the account. There is no circularity in the account of moral goodness provided by DCT. The account does not identify moral goodness with resemblance to a being that has such-and-such properties, or more precisely the property of greatness to a maximal degree or a maximum degree. Rather, the account identifies moral goodness with resemblance to God, the maximally great being that actually exist, with respect to some relevant qualities.
In the case of the meter, the way of identifying the paradigm was to say it was the distance between two lines on that bar, over there in Paris. 
In the case of moral goodness – or even greatness -, the way of identifying the paradigm is to say it's the greatest conceivable being, that being who actually exists.
What's the problem?
Alice: In that case, the definition of 'God' as 'the greatest conceivable being' only plays a role as a means of identifying the object that is the paradigm, and it's not essential to the account. That avoids circularity but still leaves us in the dark as to what moral goodness is.
Bob: I don't agree.
Alice: Let us assume now and for the sake of the argument that there is an omnipotent, omniscient, maximally loving and kind being. Let's call that being 'Jane' – that's just a proper name I'm using here. To be clear, I just picked an – assumed – actual being by listing some of her properties - enough properties to identify her uniquely -, and then used a proper name – Jane – to name that being.
Let us now pick the meter bar in Paris – that specific bar, which is still over there, in Paris  – and let's define 'oldmeter' to be a distance equal to the distance between the two lines on that bar. That is a stipulative definition. Let us call the bar 'Ted'.
I have three questions:
2. Why is Jane maximally great?
3. Why is the distance between the two bars on Ted one oldmeter?
1. Jane is God, 'God' is defined as the greatest conceivable being, and it's a conceptual truth that maximal greatness entails moral goodness. So, Jane is morally good.
2. Jane is God, and 'God' is defined as the greatest conceivable being. So, Jane is maximally great.
3. Ted is the bar over there, in Paris , because that was stipulated – i. e., 'Ted' is the name given to the bar - , and 'oldmeter' is defined as the distance between the two lines on the bar over there, in Paris . So, the distance between the two lines in Ted is one oldmeter.
Alice: Do you see why your reply to the third question is very different from your reply to the first and second questions?
Bob: No. Why?
Alice: Your reply to the third question actually informs me why the distance is one oldmeter, by explaining to me how 'oldmeter' was defined, and that 'Ted' is the name given to the bar, etc.
On the other hand, your first and second replies leave me in the dark as to why Jane is morally good, or great, let alone maximally great.
In fact, given your definition of 'God' as 'the greatest conceivable being', the first part of your replies – namely, “Jane is God” - actually means “Jane is the greatest conceivable being”.
But I'm asking why Jane is morally good, and why Jane is maximally great, so insisting that Jane is the greatest conceivable being leaves me in the dark as to why Jane is maximally great, or morally good. Your reply is uninformative.
From a slightly different perspective, the term 'oldmeter' is stipulatively defined as a distance equal to the distance between the two lines on the bar over there, in Paris , so if somebody asks why the distance between the two lines on the bar over there, in Paris , is one oldmeter long, it is a proper reply to explain that 'oldmeter' is defined as a distance equal to the distance between the two lines on the bar over there, in Paris  – and of course, that distance in question is equal to itself. [b]
On the other hand, the terms 'morally good', and 'great' are not defined in any way in DCT– they are ordinary terms[c], and left undefined -, so it would be improper to answer the question of why the only omnipotent, omniscient, maximally kind and loving being that exists, is morally good – or why she is great – by bringing up a definition of God in terms of greatness and saying that the being in question is God.
In his reply to Harris, Craig says that asking why God is good is like asking why bachelors are unmarried. Yes, granted, as long as one keeps that definition of 'God' as 'the greatest conceivable being', it would be like asking why bachelors are unmarried, but on the other hand, asking why Jane is good, or why the only omnipotent entity that exist, or the creator of the universe – that specific entity, assuming she exists – is morally good, is not at all like asking why bachelors are unmarried.
If DCT is to avoid vicious circularity, it can't rely on the 'greatest conceivable being' definition of the word 'God' to answer questions like the ones I asked (e. g., 'Why is that being morally good?', 'Why is that being great?').
Bob: I don't think that Craig made any mistakes in the context with the debate with Harris.
Of course, the ball has to stop somewhere, and for Craig – and for me – it stops with God.
Alice: But again, that leaves us in the dark as to why Jane is morally good. It's uninformative.
Bob: It is somewhat informative. But how much information we get is an epistemic matter. Craig's metaethical argument is an ontological metaethical argument. The account does not need to be as informative as, say, “water is H2O”.
Alice: In that case, I have another question:
4. What makes it the case that Jane maximally great?
This is a question about truth-makers. What makes the statement 'Jane is maximally great' true?
Remember, I stipulated that Jane is the only omnipotent, omniscient, maximally living and kind being that exists.
Bob: Jane is maximally loving and kind, and those are all great-making properties, which she has to a maximal degree. Jane also has power and knowledge to a maximal degree – that's all great-making.
Moreover, Jane is also maximally morally good – moral goodness is another great-making property -, and generally, Jane has all of the great-making properties to a maximal degree.
That's what makes it the case that Jane is maximally great: the fact that she has all of the great-making properties to a maximal degree.
Alice: Alright, so here's another question:
5. What makes it the case that Jane is morally good?
Remember, moral goodness is a great-making property, so it can't be that greatness is a morally good-making property. That would be viciously circular. So, what makes it the case that the only omnipotent, omniscient, maximally kind and loving being – i. e., Jane -, is also morally good?
Bob: Jane is the paradigm of moral goodness. To be morally good is to resemble Jane in some respects. And of course, Jane resembles Jane.
Alice: But what makes it the case that Jane is the paradigm of moral goodness?
Unlike the meter and the meter bar, 'moral goodness' is not defined in terms of Jane.
Bob: It is a necessary brute fact that Jane is the paradigm of moral goodness. The ball has to stop somewhere. Jane is God. The ball stops with God.
Alice: Okay, so the point remains that DCT is different from the 'oldmeter' identification in that we get a proper explanation as to why the distance between the two lines on the bar is one oldmeter, but on the other hand, DCT leaves us in the dark as to why Jane - the only omnipotent, omniscient, maximally good and kind entity that exists - is the paradigm of moral goodness. It provides no explanation whatever.
Bob: Again, whether the account provides us with a good amount of information – like “Water is H2O” - is not the point. You're confusing ontology with epistemology. The point remains that theism provides an ontological grounding in the sense that there is some being that exists in the mind-independent world and that serves as a paradigm of moral goodness. Without God, there would be nothing in the world that would make moral statements like 'Agent A is morally good' or 'Agent B has a moral obligation to do X' true, or at least objectively true.
Alice: But why not?
As I already explained, there is no burden on a non-theist to provide an account of objective moral values or duties in terms of informative identification. But given that you claim that there would be no objective moral values or duties without God, then it's up to you to show that no potential account would succeed.
For example, moral goodness – as a character trait - may well be a complex property, involving having such-and-such dispositions to act, feelings, etc., described without using 'morally good' or any moral [or not clearly moral; that's a variant] terms. Moral goodness in the sense of 'a good situation', etc., is handled similarly, identifying it with some features of the situation, resulting in two big disjunctions of conjunctions. And if you want a unified account – which I'm not sure is a good idea, but that aside -, then a disjunction of the two disjunctions can do the job.
In fact, the view that being a morally good person is the same as being disposed to be kind in such-and-such situations and to such-and-such agents, being caring and loving – or disposed to be caring and loving, etc. - in such-and-such situations, and so on – or something along those lines -, seems intuitively plausible.
On the other hand, the idea that to be morally good is to resemble a certain being in certain respects is much less plausible, not to mention the fact that we have excellent reasons – decisive ones – to conclude that such being does not exist.
To be clear, I am not committed to the informative identification of moral goodness that I sketched above. I have no problem recognizing that I do not know what the objective foundation of moral goodness is (see, for example, this post). The sort of identification I just suggested is just one option. My point is that perhaps moral goodness is that, and at least that identification is no less plausible than the identification contained in DCT, and no less informative.
Granted, without identifying the 'such and such', and the 'etc.', the account I suggested does not provide a very informative account, but again, there is such burden on my part (see, for example, this post), and moreover, the account provided by DCT is not more informative, since it tells us that to be morally good is to resemble God in some respects, but it does not specify what those respects are, the extent of the resemblance, etc.
Now, this view may have necessary brute facts, but so does DCT.
Bob: So, you think that that account of moral goodness is correct?
Alice: No, as I said, I take no stance – I just claim it's more plausible than the account provided by DCT. But you claim that there would be no objective moral goodness without God, so you have the burden to show that the account I suggested is false.
Bob: The problem is that without God, there would be no paradigm of moral goodness. Nothing would act as a measure of moral goodness. Without a paradigm, who or what would determine what is morally good? For example, in your account, the 'such-and-such' is not specified. But without God, who or what would determine what goes into the 'such-and-such'?
The answer is that nothing would, and moral goodness would be subjective.
Alice: But why would a paradigm be needed in the case of moral goodness, but not in other cases of objective properties?
Take, for example, the case of cruelty (for more details, see this post). There is objective cruelty. But there is no good reason to suspect that there is a paradigm of objective cruelty – if you think otherwise, why, and what is it?
So, why would the fact that there is objective moral goodness give us good reasons to think that there is a paradigm of objective goodness?
You have not provided any good reason to think that there is a paradigm of objective moral goodness, or to think that whether there is objective moral goodness depends on whether there is a paradigm of objective moral goodness.
[a] I posted a more thorough reply to Craig's metaethical argument elsewhere. Some parts of it are outdated, in the sense that I would write them somewhat differently if I did it now, but for the most part, I would make the same arguments today.
Still, some of the arguments are improved and/or more thoroughly developed in the dialogue above. I'm writing a longer post, which will address more potential objections from a defender of Craig's argument, but I don't know when it will be ready.
[b] One might use a more precise definition in order to deal with questions like 'What if the bar is heated? Does an oldmeter remains the same?', but that is not necessary in this context. In any case, one may just stipulate for the purposes of the example that 'oldmeter' is the distance between the lines in question even if the bar is heated.
Mark Murphy, “Theism, Atheism, and the Explanation of Moral Value”, in “Is Goodness Without God Enough: A Debate on Faith, Secularism, and Ethics”, edited by Robert. Garcia and Nathan King.
Also, Morriston explains what Craig means by 'ontological foundation' or 'grounding' in “God and the Ontological Foundation of Morality”, Religious Studies (2012) 48, 15–34 f Cambridge University Press 2011