"Multiplayer" or "Online Multiplayer". Pretty common in the days before WoW. They didn't invent "MMO" (was that Ultima?), but people called those a lot of different things, like "MUD" or "MUCK", because the niches played differently. MMO became a catch all around the time of WoW, though. Made for a clear, simple distinction between internet scale player count games and countable concurrent player games.

Edit: didn't realize you were the author, asking a practical question about how to describe your project. Sorry about that. For that, I personally think you're fine. You're trying to tell people what it is, not be super technically accurate.