Such a dichotomy does not exist. Whether it's a game or not depends on the intention.
Discussion
Whose intention?
Good question. I don’t have an answer for that. Most likely everyone’s who got one towards what you consider to be the game.
Mirrors on the ceiling, the pink champagne on ice
And she said, "We are all just prisoners here of our own device"
And in the master's chambers, they gathered for the feast
They stab it with their steely knives, but they just can't kill the beast
Last thing I remember, I was running for the door
I had to find the passage back to the place I was before
"Relax, " said the night man, "We are programmed to receive
You can check out any time you like, but you can never leave"
☝🏻🐸