I would use Minecraft as a counterpoint considering it’s perfectly reasonable that someone could play the game exclusively online using nothing but community servers while completely ignoring all single player experiences (which I’d argue hasn’t truly existed in a long time since the game now hosts a local server which you connect to during “single player”), but I get the feeling you’d still take issue with that example because it does still have a single player experience you could do.

So for a (as far as I recall, it’s been years since I last played it) multiplayer only experience: TF2 and its community servers. Valve could shut down all of their own servers for TF2 tomorrow and (aside from a hiccup in operation with making a server to distribute the list of community servers or making some other work around) the game would still have a thriving online community.