It's actually an interesting exercise. Ethics comes up constantly in contemporary phil-rel, and whenever it does it's worth asking what kind of ethics has to be true for the arguments to work. It's often obvious that the ethics being assumed is not consistent with any of the most commonly accepted forms of ethics, some obscure variant that may, for all one knows, be perfectly justifiable, but whose use is never justified despite not even having the excuse of being common. In other cases, it's not clear what ethics you could have that would make the argument work. I've come across cases, usually in the wilds of the internet, but real cases by actual philosophers nonetheless, in which it seems very much as if the ethics has to be changing in the middle of the argument -- a strict consequentialism to get this step, a strict deontology to get that one. In other cases, the problem doesn't seem to be incoherence so much as obscurity -- it's just not clear what ethics is operative in all these ethical judgments, at all.
In this case, for instance, Houston rejects the notion that God could require morally horrific actions (it is never explained what exactly is being taken to constitute an action as horrific, although murdering is given as an example and it is supposed to have something to do with "beliefs that are most central to the core of one’s moral convictions", although it is never said whose beliefs are being counted) by appeal to Kant:
For Kant, it seems that such commands carry with them the inherent transparency of their not being from God, and therefore they must be regarded as illusory. Thus, in The Conflict of the Faculties, Kant says of the man who hears a voice commanding him to violate the moral law, that he must doubt that advice: “for if the voice commands him to do something contrary to the moral law, then no matter how majestic the apparition may be, and no matter how it may seem to surpass the whole of nature, he must consider it an illusion.”
All well and good; it is pretty clear that Houston's argument would require the rejection of consequentialisms of all sorts (although at one point he does frame it in terms of consequences), and his argument also won't work on any kind of positivist deontology, like divine command theory. So it would make sense that he is assuming a Kantian view of morality, and thus we get Kant.
On the other hand, he goes on immediately to argue "God can and does owe things to the men and women he creates." As I've noted before, there is no widely accepted theory of obligations on which it makes sense to think of God as the kind of moral agent who would have obligations -- on most theories of how obligations work, it would be a category mistake to say that God owes anything at all, unless we are using the term in a way much looser than Houston's argument would require. But the most relevant thing here is that Kant's theory of obligations is very definitely one of the theory of obligations in which God has no obligations and therefore owes us nothing. We have obligations because there is a possible disparity between our wills and moral law; but this disparity does not exist in the case of God, who has a holy will. God's will is just an expression of moral law itself. And this is directly relevant to the argument that Kant just gave. We know that it's impossible for God to command something like sacrificing your son, Kant thinks, because God's will, being holy, directly expresses moral law without the kind of gap our will has to overcome; the moral law, being the categorical imperative, is something we directly know; and we know that the moral law imposes no such requirement. Thus God's will can impose no such requirement. Thus it makes perfect sense for Kant to give the argument that Houston quotes; but the whole argument in Kant depends crucially on the fact that God's will is not even the kind of will that could have an obligation. So in a very brief space Houston has used an argument from Kant to draw a conclusion and then denied one of the assumptions that Kant is making in the argument to begin with.
Now, of course, it's entirely possible that there is some other foundation by which you could have the Kantian argument without the Kantian assumption. But the point is in a different question: How could we know it? The ethics being assumed as absolutely obvious and definitive appears to be a definitely nonstandard deontology that's inconsistent with the most common major forms of deontology, and we don't know enough about its details to say whether it is better justified than the more common forms. We don't really know what it is at all, or how it works, or why it is giving us this particular set of arguments. This is a minor example, but as I've said appeals to ethical considerations in philosophy of religion are sometimes considerably more egregious in their failure to explain what the ethics actually is. (Houston at least gives us a few definite pointers, so we can guess that it's probably a deontology somewhere in the vicinity of Kant although not strictly Kantian, and it requires assuming that people generally share a "fundamental moral intuition" about murder; that's more definite than you sometimes get.) Whenever we look at arguments in philosophy of religion that appeal to ethical considerations, we always need to stop and look closely at the ethics in the background.