Those are my exact thoughts after watching DeepMind's LLM poker tournament. LLMs aside, current game-theoretic reasoning approaches in CS literature for imperfect information games are all centered around CFR, which is a brute force algorithm. For real reasoning, LLMs need to understand underlying game dynamics and reason up optimal strategies from first principles, which I believe is what you're saying with autonomously producing the right abstractions (instead of cribbing them from somewhere else in this case being running CFR, for example).
I was thinking for a while that this specific capacity needs to be unlocked for "real" intelligence to emerge, but I recently opened my mind to the idea that it's just downstream from math reasoning—and we're making progress there. What are your thoughts on that? Do you think that something needs to occur on top of math reasoning improvements or does a step-shift need to happen to get those improvements in the first place?