Amazing puzzle game!
The idea is really creative and really well implemented. I was a little lost at first on how the game works, but, after some trial and error, I understood it and it became quite fun.
The music is great. Calm and doesn't get on your nerves even when you are wracking your brain over the puzzle and maybe a bit frustrated. I find that to be a great thing for a puzzle game to have.
The fact that you made working saves is also a great plus, specially for a game jam game.
My main suggestion is that the game could use a detailed tutorial on the beginning to let the player understand how the mechanic of looping moves and steps work.
All in all, great work!