When you play Dolmenwood[1], for example, as a TTRPG setting and group of modules, no table will play the same game, but they are all playing Dolmenwood. So I guess it would depend on how much you can get the LLM to adhere to your setting and rules.
Heh, I was just browsing Exalted Funeral for unrelated reasons!
Re: TTRPGs... I think that's difference. There's no expectation that when two groups play a D&D session, even with the same module, that the story will play out the same (note: I never played one of those strict adventures with predefined story beats).
But with computer games, which includes Interactive Fiction (the modern name for text adventures), you do expect the same experience. People remember Planetfall because of the story and how it plays out. People remember that in Colossal Cave Adventure there was "a maze of twisty little passages, all alike", so much so that it became a bit of early internet/hacker knowledge.
I think you lose this if the LLM is making up too much stuff, and so far it's proven very hard to reign them in.
[1] https://www.exaltedfuneral.com/pages/dolmenwood Yes I'm plugging this, but I am not financially involved.