I checked, and I do see a response to his general claims, but not to the specific point I’m asking about. I’m talking about the objection that claims the cosmological argument relies on the ontological one, and that since God’s existence is not necessary, it collapses.
If I’m not being clear, here’s a short 5-minute video that explains it well:

Thank you very much.

I listened, and here are my comments:
1. I don’t see why the cosmological proof assumes God’s necessity. In my view, it does not.
2. He defines factual necessity as constant existence. That’s a strange definition, because it has nothing to do with necessity. Something non-necessary could still exist at all times. But that’s just semantics.
3. He says the cosmological argument depends on the ontological argument. But there are two problems here: a. So what? Maybe both are actually correct. b. It’s not true that there is such a dependence (see 1). c. It’s not true that logical necessity must stem from Anselm’s ontological argument. Maybe there is another ontological argument, or another argument that leads to logical necessity.
4. When he moves to modal necessity, he again ties it to logical necessity. That is, of course, nonsense. He is simply adopting the modal interpretation as the meaning of logical necessity, so in fact there is no additional kind of necessity here. It is logical necessity. So, very conveniently, he rejects it in exactly the same way he rejects logical necessity.
By the way, chapter 3 of the Proslogion proves God’s logical necessity through an additional ontological argument. There is no need to use chapter 2 (which proves only existence) and extend it.
5. At minute 3:30 he falls into a fallacy that I have pointed out before. He infers impossibility from lack of logical necessity. See column 580.
6. He makes the same fallacy regarding factual necessity. There he concludes that if something is factually necessary but not logically necessary, then it is necessarily impossible. He does not even offer an argument for that conclusion. But it is not true. See that same column.
7. The statement at the end that without the ontological argument it is impossible to ascribe necessity to God is delusional. There is not a shred of reasoning there.

In short, it has been a long time since I heard such a collection of nonsense, and when it is said with such confidence, it strikes me as even more ridiculous.