Amazing idea! I love how you don't even explain it, you just let the player stumble onto it.
I also loved the little touches of having the camera follow the hat instead of the player and making the player the same color as the ground. It makes the hat the center of your attention and you even forget you're playing as the cube, you just care about getting that damn hat in the time vortex at the end =D
This is a really great game, congrats!