All right it did feel like a retro platformer all right, it is a cool little game. You do explore that one mechanic of levers thoroughly.
Now couple of things I've noticed while playing.
The hit box around the levers could be a bit bigger, they are hard to hit while mid air.
You could add coyote time and jump buffering to your character, the jumping would feel more natural.
Overall good work! That "Run" section drained the life out of me but was well made, actually stressful :D