Huh, seems like copy-pasted link to older video, and that for some reason doesn't display preview correctly? Anyway, here is the latest
youtu.be/gJEU-0o2z9s

Under the hood it runs on this library enet.bespin.org (reliable UDP). On top of that most of what is sent is player's orders, which is just the "deterministic lockstep", so I wouldn't go as fas as "invented"

Yes, custom. It started as a learning project, so I went that way. Using one of the big engines would be much faster though :)