How to walk through walls using the 4th Dimension [Miegakure: a 4D game]

Aren't 3D games already 2D, as they are just projecting 3D world onto 2D plane? Alternatively, taking 2D intersection of 3D world would lead to something like 2D/3D mode of Miegakure: ▶ this video

For those wondering, Miegakure is a not-yet-released 4D puzzle platformer. Think Flatland but as a 4D video game. ▶ this video

The test in the article was extremely easy for me, I guess I can visualize better than most people (I had no idea some people have trouble with that). It's funny, because I've considered myself to be an "auditory" person. Something I tried to visualize recently, and found quite challenging, was trying to remember this video: ▶ this video I watched it a couple of years ago, and last night I replayed it in my head, but with great difficulty.

The plane exists - it is passing through the character body (perpendicular to the ground) and parallel to the desert, grass border in the example video. You can see when the 4D rotation occurs there, that in that plane, everything stays constant (e.g. rocks stay there, trees, etc.) You just look at the objects from different angles as it rotates. Edit: Link to the relevant point in the video - ▶ this video