Hi
There are already some 4D games, I just released a basic new one.
You can try it online on page https://www.raktres.net/tak4d/, tab "maze" (don't miss the "help" button on the right!).
Generally, 4-dimensional spaces are represented through a single projection. The idea here, is to use the principle of multiviews for technical drawing and represent an object through several projections.
4-dimensional space is therefore seen through 4 projections (or cuts) on 3-dimensional spaces.
Using this idea I had already made a simple polytopes visualization tool a few years ago (I started rewriting it on "viewer" tab). I used the principle to make this maze game. It is very basic, movements are limited to the 8 main directions, and the levels are currently very small.
It is better to try it on a PC, the interface is not very suitable for smartphones.
Hope you find some fun there.
Jeff