Why is it we don't call videogames "4D" if they also operate through time?

Animations are four-dimensional. Colored animations are seven-dimensional. More if they include surface normals or lighting information. Simple.

I guess if moving through time other than forward like normal it'd justify calling time a new dimension on which you can play on.

Otherwise, we just focus on the 3D space they represent and take time for granted

3D Gaussian splats are still images of 3D space / photogrammetry

So I'm guessing it came from representing the additional dimension