Some of the scenes from the video remind me of Manifold Garden [1] - only 3D but a 3-torus [2] and you can change the direction of gravity, i.e. what is up and down. And also visually beautiful.
The additional code he wrote to make a 4d game work in the Unity game engine is available on github and MIT licensed: https://github.com/HackerPoet/Engine4D
When I first saw the title, I assumed this game was implemented in the same engine. I believe there are a few already.
Steam link: https://store.steampowered.com/app/2147950/4D_Golf
The person goes over quite a few technical details on their Youtube, though they talk about a bunch of other coding experiments too.