First, that got to be the most adorable, and the most badass cube I've ever played as!
Second, this game scratches an old itch... to play an old-school game, with a nineties feel; harkening to back when the platform games were flourishing.
I like Gappy's moveset. It feels so fluid, I can forgive the little slipperiness of the cube's movement. Besides, the levels have a lot of room for adjustment, anyway.
Also, the double jump can always be done once after any of the other jumps. It feels like it would make Gappy overpowered, yet the levels are full enough of dangers that the player is going to need the ease to use. The dive move is more useful than I gave it credit for.
One critique I have is the loading time after losing a life. In my opinion, it could be a bit shorter.
Also, in the second level... took some time for me to find the doors, since the background is dark. Thought that the colored squares were items of some kind.
People suggested that there be more checkpoints. The suggestion of an easier mode with more of them gets my support.
The difficulty is good, even if I'm having some trouble (need to git gud). Glad to see that you weren't afraid to put lethal hazards, like the water and the buzzsaws. I think that learning to avoid them is part of the gameplay.
I'll be tuned for when the game is out. Look forward to see it finished.