>> Nobody can assess the entire game tree, so the fact that it is theoretically knowable isn't actually relevant in a game.

That's not the point though. The point is that you only need to consider current state when considering your next move in Go or Chess. This is not the case in an incomplete information game, since the sequence of moves that led to the current state contains a lot of information. That's not the case in Chess or Go. Basically, Chess and Go satisfy the Markov Property, while Poker does not.