This could be fun with some more enemy types and some choices you have to do when you reach a set of 3 doors. Maybe make it infinite with some more abstract goals?
A few things that felt a bit rough:
* Entering a room with a demon gives you about half a second where your controls aren't locked and you can move around.
* I dont think you can time out on the minigame.
* The ending screen (with the cage) is a bit ambiguous, I think it could benefit from a "return to main menu" button to show the player they've reached the end, and would allow them to start over.
* Seeing the same animation roughly 15 times gets a bit dull when you have to walk back and forth between rooms to respawn the demons.
* If you win the first minigame you dont get any magic, which isn't really explained and doesnt really benefit the player (aka you can be *too* good at the game).
I think this has a lot of potential, hope you keep working on it!