I don't think this is right: To calculate the optimal path, you do need to model human cognition.
At least, in the sense that finding the best path requires figuring out human concepts like "is the king vulnerable", "material value", "rook activity", etc. We have actual evidence of AlphaZero calculating those things in a way that is at least somewhat like humans do:
https://arxiv.org/abs/2111.09259
So even chess has "hidden state" in a significant sense: you can't play well without calculating those values, which are far from the surface.
I'm not sure there's a clear line between chess and poker like the author assumes.