If not three, then how many dimensions? One could argue that both the video games and the physical puzzles are in 4D space-time, but I doubt that's what you me

If not three, then how many dimensions? One could argue that both the video games and the physical puzzles are in 4D space-time, but I doubt that's what you meant. The space within the video game isn't flat / Euclidean of course, but that doesn't mean it's not 3D.