Poker is nowhere near as deep as chess, but it's deeper than you're making it sound. It's not just about reading people, especially for Texas Hold'em. Knowing probabilities and how many outs for both your pocket and flop, turn and river, taking your betting order/big and small blinds/your remaining chip stack/whether someone raised for whether you should enter the hand or not, knowing when to fold, etc.
All of that can be done without reading people at all. In fact in online poker, there's not much reading of your opponent you can do usually, just judging based on their previous actions.
I wouldn’t really say that’s a fair assessment either. I don’t think it’s in any way clear that Chess is deeper than Poker, or even by what metric you would determine such a thing.
Certainly in both games there are no competitors, human or robot, that has solved the game.
All of that can be done without reading people at all. In fact in online poker, there's not much reading of your opponent you can do usually, just judging based on their previous actions.