Don't get me wrong, the question of whether this or that game is better with or without win conditions is perfectly interesting. It's just the raw "is it a game or not?" that's not useful. It's like asking whether comic books are books - the answer is "yes under some definitions, no under others", simple as that.
For the case of your game[0] specifically, one option is to expose game stats that the player can form their own challenges around. E.g. if the game UI shows how many times you've jumped, that implicitly lets the player form "do X without jumping more than Y times" sorts of challenges, etc. Or the more formal way to do it is like e.g. Minecraft achievements - there's no "win condition" for putting a saddle on a pig or whatever, but the mere fact that there's a piece of UI tracking whether you've done it or not, creates a challenge by itself.
I've thought about that - and it's not that big a jump to have a GUI that allows a user to specify a win condition (and locations to traverse, other conditions etc). Then, the user can share it online. I haven't played GTA V online, but I think it does something like that.
But actually, I don't want those sort of win-conditions for this particular game, not even DIY stats. It's just an immersive simulation. Guess I'm just not too sure it WILL be immersive or engaging - even for me to play! Just have to see, I guess.
Taking your lead, I suppose if a movie can be immersive, why not a "game" which has no win-condition? But the moment I say that, I immediately realize that movies do have "win-conditions" - just of the protagonist, not the viewer/player. Goals, stakes, motivation, obstacles are all important narrative components.
Can you have an immersive movie without narrative? Sort of maybe, some experimental/arthouse, but they aren't very popular (and arguably do have some kind of narrative).
You're probably right about definitions, but they do inevitably lead to the components of a game/non-game, and whether they are engaging, and what makes them engaging... and they're easy to ask.
For the case of your game[0] specifically, one option is to expose game stats that the player can form their own challenges around. E.g. if the game UI shows how many times you've jumped, that implicitly lets the player form "do X without jumping more than Y times" sorts of challenges, etc. Or the more formal way to do it is like e.g. Minecraft achievements - there's no "win condition" for putting a saddle on a pig or whatever, but the mere fact that there's a piece of UI tracking whether you've done it or not, creates a challenge by itself.
[0] yeah I said it! ;)