Literal interpretations are the best interpretations. Our games have the same idea though min is a platformer with some other gimmicks thrown in.
The restrictions on the player create the puzzles. You have a lot of potential actions for the player to take. The button swapping mechanic is quite cumbersome(though it's not like mine is any better. Though in this case the potential for player confusion is higher due to the large amount of buttons.
The most annoying ones were the arrow ones. They could be turned into static tiles in the map that change your direction when stepped on. In fact, there is probably a game that does just that.
the art is minimal but it fits the game. Music is also nice. I have no real complaints here.
Overall, great job!