Interesting.  Reminds me of Getting Over It, but slightly less awkward.  Still too awkward for my tastes, but I guess some people might be into it.

One suggestion I would make is to add a bit of Coyote Time - a moment or two after falling off a ledge where you are still considered "grounded" and can still fire the gun twice.  It can be hard to tell where the ledge actually is, and the round shape of the player character makes it hard to tell when you are "on the ground", so this would help provide feedback in areas with uneven terrain and would make the game a little less frustrating.

The credits screen seems bugged. It moves at a snail's pace and there doesn't seem to be any way of leaving the screen.