Generate incrementally using a pathfinding system for a bot to move around and "create the world" as it goes, as if a Google street view car followed the philosophy of George Berkeley.
Except this time there is no underlying consistent world, so it would be up to the algorithm to use dead reckoning or some kind of coordinate system to recognize that you're approaching a place you've "been" before, and incorporate whatever you found there into the new scenes it produces.
I suppose this is the easy part, actually; for me the real trouble might be collision based on the non-deterministic thing that was generated, i.e. how to decide which scene edges the player should be able to travel through, interact with, be stopped by, burned by, etc.
Consistent inconsistency gets old very very fast.
Best case: roguelike adventure.
But generally just phantasmagoria.
I know you didn’t mean it like this, but this is kind of an insult to the insane amounts of work that go into crafting just the RNG systems behind roguelikes.