Regardless of whether or not this constitutes a Dungeon Crawler with the grid size, this was pretty nifty concept for a game, and I feel like you only just scratched the surface in terms of how controlling the two sides at once can be utilized.
Things like deliberately utilizing the environment to desync your movements, or puzzles with cross-dimensional effects. There's something in this.
Also, do mein ears deceive me, or is that a Bill & Ted guitar lick?