This is amazing. It matches the description I read in Michio Kaku's Hyperspace as a kid. Except the visuals, although similar, were said to be blobs. I'm not sure.

I like that the game creates the ability to move through a 4D space while seeing the effects in 3D. The fundamental is great. Also, how a 4D person might move through walls via the fourth dimension. I think an even more interesting angle might happen if a game tries to break the assumption that 4D movement is wide open: put obstacles in the way where a person must use intuition to navigate it by making a 2D/3D map of that space as well. Maybe the game does that, too.