This is really, really clever. When it finally clicked that I could walk into walls to shift the keys around without moving, it made me feel smart for figuring it out, something that's really important in a good puzzle game.
A small UI tweak I might make is to have the grid and your current location on it visible somehow. It's easy to get lost by wandering into walls, especially since without an ortholinear keyboard things don't quite line up like they're supposed to.
The minimalist aesthetic works great here, allowing the player (and I imagine you as a creator) to focus on the levels themselves. Very good work.