This sounds rather silly. Given the usual definition of AGI as being human like intelligence with some variation on how smart the humans are, and the fact that humans use a network of neurons that can largely be simulated by an artificial network of neurons, it's probably twaddle largely.
Yes, the simpler versions of your argument is that the article is basically stating that "human level intelligence is mathematically impossible" (to stick with that fuzzy definition of AGI). Which is of course easily refuted by the fact that humans actually exist and write papers like that. So, the math or its underlying assumptions must be wrong in some way. Intelligent beings existing and AGI being impossible cannot both be true. It's clearly logically wrong and you don't need to be a mathematician to spot the gigantic paradox here.
The rest is just a lot of nit picking and what not for very specific ways to do AGI, very specific definitions of what AGI is, is not, should be, should not be. Etc. Just a lot of people shouting "you're wrong!" at each other for very narrow definitions of what it means to be right. I think that's fundamentally boring.
What it boils down to me is that by figuring out how our own intelligence works, we might stumble upon a path to AGI. And it's not a given that that would be the only path either. At least there appear to be several independently evolved species that exhibit some signs of being intelligent (other than ourselves).
Whether human thought can be reduced to the actions of a network of neurons is still an open question.
https://en.wikipedia.org/wiki/Mind%E2%80%93body_problem
Can you justify the use of the following words in your comment: "largely" and "probably"? I don't see why they are needed at all (unless you're just trying to be polite).
It's just it's imprecise like with the brain can "largely be simulated by an artificial network of neurons" - there may well be more to it. For example a pint of beer interacts differently with those two.
I see the paper as utter twaddle, but I still think the "largely" and "probably" there are reasonable, in the sense that we have not yet actually fully simulated a human brain, and so there exists at least the possibility that we discover something we can't simulate, however small and unlikely we think it is.