I believe the difference is that Miegakure actually has real puzzles that involve things you could only do in 4D.

But in Fez the 'extra' spatial dimension was the third, which is one we're used to existing in and manipulating in real life. THIS is an instance of a game allowing us to do something we've never done before - rotate things in the fourth spatial dimension.

And then this game would be 5D, and the point would still stand.