We do not know if it is even possible to see clearly all external physiological stress markers on the other players

See an example for one stress marker. That’s an order of magnitude above noticing blushes. Dogs have much better sense of smell, and technology exists to simulate that. You can probably detect the pulse of each person in a noisy room with just an array of sufficiently-accurate microphones.

Note that human intellect was sufficient to discover the technique, and the technique is powerful enough to allow human senses to see the movements directly, you don’t even need to examine Fourier transforms and the like.

Humans can't predict the behavior of dogs or chimpanzees and they're operating on a level way below ours.

I can’t and you can‘t. But dog and chimpanzee experts can predict lots of things I couldn’t. And experts on human behavior can predict lots of things about humans that might seem impossible to non-trained humans. Psychiatrists and psychologists can often deduce with decent confidence lots of things from seemingly innocuous facts, despite the mess their discipline might be in bulk. Sociopaths can often manipulate people despite (allegedly) not feeling the emotions they manipulate. Salesmen are often vilified for selling things the buyer doesn’t want, and the fact that there exist consistently better and worse salesmen indicate that it’s not just luck. Hell, I can predict lots of things about people I know well despite not being smarter than them.

Note that the hypothetical poker player (or whatever) doesn’t need to predict perfectly. They just need to do it much better than humans. And the fact that expert human poker players have been known to win poker tournaments without looking at their cards is evidence that even human-level prediction is hugely useful.

Hell, Eliezer allegedly got out of the box using only a text channel, he didn’t have the luxury of looking at the person to judge the emotional effects of his messages.