Miegakure [Hide & Reveal] is the first game that lets you explore and interact with a 4D world. In this game, the fourth dimension is not time! It is an actual fourth dimension of space, that works just like the first three dimensions we are familiar with. If you count time, this game is 5D.
Amor fati asked about higher-dimensional games [ > ] and this one came to mind. Development on it started at least as far back as 2010.