I did something faintly similar ages ago with an RPG world editor, project used such old tech that it's long abandoned. I did it over lan, and gave each user their own map file which overrides the main map as it's loaded. So if you imagine having your standard level map, I had an extra one for each user, then the main map will be loaded, then all the other users, then the current user on that PC's map. One user is designated boss, and their PC saves the main map data then it's safe to delete those extra map files. I think that's quite a good option for working on lan with a small team, I only got to test mine with 2 other users, but it was pretty fun to work like that.
The main thing, is that level design is tedious and daunting. I don't think any professional would design a map by themselves, at least not one as intricate as the one shown in the videos. Instead of the usual drudgery, it could be a party instead! - at least over LAN. Personally, I'm not sure I would trust the internet to look after big world files, at least if they are just sitting in a network location, it's quick to back them up and come up with systems to look after your file saving.