Nice implementation of the wall-climb mechanic! I'd suggest zooming the camera out while climbing due to the vertical movement. There were also some minor bugs with it (such as when hitting an upper corner of a wall), but otherwise it worked well.
When the game restarts after death, the energy is kept, but keys are not. It makes retrying a little easier, but the lack of checkpoints still makes it annoying when only one hit kills the player.
In any case, good work! I like the custom game mechanic implementation the most.