Of course, if we look at people who unequivocally fall under the label 'classical theist' in the history of thought, none of them actually set out to do this; and it's difficult to identify any who can even plausibly be regarded as doing this. And that is where Webb's error lies. 'Classical theism' is a classificatory label; it is a category under which various positions fall if they meet certain criteria. But it does not follow from this that classical theisms are nothing but whatever it is that makes them meet those criteria. That would be like thinking that because mammals are warmblooded animals with hair and female mammary glands for nourishing young, and because human beings are mammals, that the whole of human life is summed up in having hair and mammary glands in the female. In reality, every classical theism is much more than just the features that make it a classical theism. And since classical theism as such doesn't set out to reduce God "to the idea that intellectuals have about themselves", the only way to say this would be to look at all classical theisms and show that, as a matter of fact, they all do end up doing this. You can't get the conclusion from general reflection on classical theism.
Of course, what Webb is really doing is trying to define a particular view as the right one, and accuse the major opposing category as trying to eliminate what he thinks are the advantages of the 'right' view. This, of course, is rarely the case in reality: positions end up in opposition not because one side is trying to get rid of the advantages of the other but because they don't think it has good reasons behind it. Not recognizing this is a recipe for tendentiousness; all Webb manages to do, for instance, is attack a position for not, according to its opponents, establishing what its opponents think important in the terms in which the opponents think it important. This is not reasoning, this is just stating a position without regard for what actually establishes it.
We see this in the comments quite clearly; Webb says at one point in the comments, "I am not saying that classical theists have no way of thinking about this, but the resurrected body is certainly a thorn in their flesh (or a very difficult concept for their minds!)." OK, but the vast majority of theologians, historically, who have held a doctrine of resurrection have been classical theists -- they were the ones who argued for and defended it against its opponents for almost all of its history A.D. So not only do they have a way of thinking about it, it doesn't seem to have been such a very severe 'thorn in the flesh' that they were tempted to get rid of it; they affirmed it over and over, argued for it over and over, insisted on its importance over and over. So in what sense is the doctrine of the resurrection any sort of problem for the classical theist, given that so many classical theists have accepted it, argued it, regarded it as important? And the answer is, strictly speaking, nothing whatsoever: none of the features that make someone a classical theist rule out resurrection of the body. Classical theism is a position about divine nature; what is more, it is a position about divine nature that by definition sharply distinguishes itself from any positions about human nature. Because of that, there is no logical bar in classical theism, as such, to any particular claim about the resurrection of the body. Classical theism is consistent with there being no resurrection. It is consistent with an account of resurrection that sees it as a reunion of soul and body. It is consistent with an account of resurrection that sees human beings as nothing but material atoms in an order and the resurrection as simply the restoration of that order to some set of atoms. Only by importing a lot of other things do we actually get any definite tendency to one such position or another. Classical theism is not a position about the human body; as one can easily guess from the 'theism'. Likewise, while classical theists generally have views about matter, classical theism is not a view about matter; thus it's mere sloppiness to say that for classical theists, "matter, being formless, is the absence of the divine". We would have to be looking at specific classical theisms -- and then it's unreasonable to take the specific case as generalizing to them all.
I'm not even going to discuss the rest of the argument, which looks very gibberish-like; much of what he attributes to classical theism is mixed up with things that classical theists have often historically rejected, precisely because of the error noted above, and that makes it almost impossible to figure out what the argument actually is, even setting aside the weird and completely unhelpful rock vs idea of rock example. His entire second and third paragraphs, for instance, are simply baffling. I definitely fit the 'classical theist' classification, and of the four names he gives I have read quite extensively in Augustine and Aquinas, have some real familiarity with Plotinus and Origen, and I have no clue what he's talking about overall. Perhaps this is just lack of clarity. But the mistake noted above definitely infects the piece.
ADDED LATER: In a further comment, Webb says:
For me, the main error, if I may speak boldly, of classical theism is its absolute separation of spirit and matter, which makes it hard to imagine or conceptualize how our bodies will be in heaven (or how heaven will be a place, or how Jesus will rule there as an embodied person). I do think that in the end classical theism undermines the idea that God is a person (it provides only the barest of resources to affirm that God is a person, as opposed to the idea that God is personal in some way).
This is an even better example of the problem than that noted above. (1) Classical theism as such doesn't commit one to any particular view of how spirit and matter are related; it's not a general position about spirit and matter but a label put on a bunch of views that share certain theistic ideas. (2) Setting aside the weirdness of the statements about heaven here, it thus follows that classical theism, as such, is consistent with any number of positions about bodies and heaven.
It is also worth pointing out, incidentally, that the people who invented the vocabulary for actually saying that God is personal in some way were all classical theists, since identifying what it is for anything to be personal in some way was byproduct of arguments for Nicene theology. Our considering ourselves persons is a backformation from orthodox Trinitarian theology, the major defenders of which, East and West, all meet the conditions for being counted as classical theists.