As some people have said before me, VN's are more like books, I mean, it's even in the name - Visual NOVEL. Of course, I understand why many people would think of VN's as 'games', but there really isn't much gameplay mechanics in your average VN (apart from saves but that's just more for convenience than anything else, like bookmarks). You could probably create a VN/Game hybrid, where the each player is a different character and they all read the same thing but from a different perspective and there are small actual games to play. But I just don't think an idea like this will work just as a VN. I mean, what's the difference between reading with another person and reading on your own, for example, when you're reading a book, you don't just let someone else read with you from the same book, you tell them to get their own (if you had common sense at least) and after that you just read seperately. You might discuss it later, but that's just discussion after reading. Besides, VN's are more for 'alone time' if you know what I mean. Initially, a multiplayer VN may seem like a good idea, but when you really look into what makes an enjoyable multiplayer game, the way VN's are just doesn't work with multiplayer.
Also regarding The Yawhg, it's not really multiplayer as it is just people reading the same story together, more like, gather around the campfire to hear the story kind of thing. There are choices yes, but it seems like it's just one guy picking the choices and the other people advise him on what to do. It's like picking a choice in Mass Effect and people tell you what choice to pick if your playing in the sitting room with friends. So yeah, not really multiplayer. More, people being told a story together. I wouldn't really call it a VN and as you said, it wasn't marketed as one. I'd probably call it more of an interactive experience with other people? It's a bit like those pick your own adventure text adventure games, a bit different from VN's. How is it different? I don't actually know how to describe it, but somebody else probably will know so I'd proabably just wait for them to appear. I guess it's the experience that's different I guess? And most people read VN's for the experience that it is. If you changed that experience it probably turns into a pick your own adventure game that I mentioned above.