I would say that hiding the puzzle from the player doesn't necessarily make it not a puzzle. As you say, if you do things identically you get the exact same game. What I mean by unforeseen is that one game I walk into a room and there are ten orcs, the next I walk in and there is a treasure chest. Whereas if it is deterministic I would walk in on the orcs in the first game, then avoid that spot in the second game (or maybe return when I am more prepared).
Perhaps in the limit that a person only plays the game for one life, it is a roguelike, but assuming they return for more lives, they have a priori knowledge that moves the game towards the puzzle genre. Eventually, given enough time, the player will learn a winning path, and there is nothing roguelike-ish in a game that i can put in a set sequence of key presses to win every time. The thing with a normal roguelike is that, while you can take a snapshot of any individual game you played and see that it is deteministic (assuming the rng will always spit the same sequence from the same seed), you only see that exact snapshot with one life.
In terms of learning the puzzle, I think it is not necessarily cut and dry whether or not you are playing a roguelike. It brings up the question of whether or not the genre of a game can change depending on who is playing it. Is a puzzle that I don't have the information necessary to solve still a puzzle?
Thinking in a different way, if the ai is as chaotic as you say, then i might argue that the game does have some sort of pseudi-pcg. I would definitely say that, when you don't have a good understanding of a chaotic system, it is effectively random from your perspective. The player is in some sense the "random seed" if they cannot accurately predict the ai response to their actions. It is in this sense that I might call the game a roguelike. After all, true-pcg isn't necessarily a must. But I think this is one of those cases where to some the game may be a puzzle, while to others it is a roguelike.
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