Yes, you just described guessing. It guesses.
Unlike people who are of course known to never hallucinate or make cognitive mistakes, or, you know, have a train of thought which is really just... a series of guess the next token... Calling that 'knowing' is in essence not that far off from what people consider 'knowing' which is in itself a deeply flawed concept.
No one is out here claiming sapience, the question is capability, and LLMs are clearly–to many of us anyway–quite capable.
Anyway, as it happens I've built an app for running games for several AI agent players, with built-in PDF support (and PDF sheets), notes, and dice. It works (until it doesn't). But I'm poking away at it anyway. I ran some Night's Black Agents on my phone last summer while sipping cider in the shade at a farm while my daughter slept and the fam was picking cherries; it was surprisingly fun!
One thing that's actually pretty fun is making characters with the AIs. They're so much better at looking up rules than my players!
I'm still playing with having an AI run a game successfully. I still find it way too easy to see the chinks and the edges of the experience. But it's getting better all the time, and some models are better in my opinion; generally speaking Claude is much better at understanding the premise of an RPG (eg. not presenting a list of options, not taking over control of my character, that sort of stuff) when system prompted properly.