No it doesn't mean that, blackjack too has an even smaller number of knowledge state (based on cards already dealt/hand/dealers card). There is a finite and small number of cards dealt and in a shoe and simple probabilistic calculation can be made to determine the absolutely correct action.

Poker is not finite, at least the wagering part of it, the interaction between the players. Even in the exact same situation as defined by the mechanics of the round, the correct answer might be different, depending on a host of psychological factors.

No. Try an analogy with chance + bluffing + non-fixed, unlimited betting + imperfect information. Better yet, try to analyze poker.

My argument is not that EVERY game with chance + bluffing is more complex for a computer than chess. It's that poker is a very different beast than chess, and it makes no sense to argue complexity based on amount of required human training. Otherwise, we'd have computers with visual perception before chess skills.