The ZUI in the video you shared is super cool. I've never seen it before. There are a bunch of folks here who have made things sort of like it. (Hopefully some of them turn up in this thread.
@westoncb comes to mind.)
While it's not a web
browser, I did make a web
site with this sort of richly transitioning navigation:
https://www.lunchboxsessions.com/explore
Click on (say) "Hydraulics", and then click on any of the "nodes". You can use the "Back" button at the top, or hit escape on your keyboard, to go up one level.
I've always loved these sorts of over-the-top transitions. I made a lot of Flash projects back in the day that each featured multiple pages connected by individually 3d-animated fly-through transitions. Sort of like the more elaborate DVD menus at the time, where each screen had a specially rendered transition. I've always loved making UIs that feel sort of
oriented in 3d space.