Well, the term "MMORPG" is really obsolete, so let's refine how we talk about online games!
There are two pieces to how players interact in online games, and these pieces are simply not talked about much. I don't even think there's defined terms for them. The two pieces are the number of players interacting, and the immediacy of their interactions.
So I'll propose some terms for immediacy, some ways to think about online games.
Pitched immediacy: When lag severely impacts how well players can interact. Usually only matters in battles alongside or against other humans, although some battles are lag-resistant and some non-battle situations might be lag-vulnerable. Due to the difficulties involved with both technology and player awareness, the number of players involved in pitched immediacy is typically pretty low.
Critical immediacy: When players interact in near real-time while tightly bound together. Lag isn't a serious issue, but a player dropping out entirely for a few minutes would be pretty serious. This is typically the "party" part of the game, and may include lag-resistant combat sections. It may also include chatrooms and so on: it doesn't require avatar-on-avatar interactions. The number of players is often quite low due to cat-herding-related difficulties.
Noncritical immediacy: When players interact in near real-time, but loosely bound. If a player drops out, the other players can continue on without much difficulty - or perhaps without even noticing. This typically includes non-party interplayer dynamics, such as wandering around a town where other players are hanging out.
Asynchronous immediacy: When players interact in a way that has a flexible gap between action and reaction, allowing players to interact without being available at the same time or place. Please note this is about interacting with players, not with the game. Skills that grow in real-time, for example, are not players interacting with other players. Messaging someone is, and the giant forum accompanying any large game is also asynchronous immediacy even though the game itself is not actually involved.
Prepared immediacy: When a player doesn't have much (or any) control at the moment of interaction, but has set it up so that things unfold according to their preference. Things like auto-shops, guilds, homes that can be visited, and "NPCified" parties are all prepared immediacy. Creating content and then allowing other players to use/experience it is also prepared immediacy. Actually, drawing fanart or making music videos may also be prepared immediacy, even though the game is not really directly involved.
Incidental immediacy: When a player interacts with other players accidentally or indirectly without really meaning to. Auction houses are a big one, here. Maintaining wikis is another. Also, in some games you can create content that is automatically reshared with others (such as Spore). This "massively single player" style content is also incidental immediacy.
Anyway, those are my suggestions.
As you can tell, every game has more than just the game. The community around the game will start up asynchronous, prepared, and incidental interactions outside of the game itself. But these kinds of immediacies can also be part of the game design from the start.
In many cases, the feel of a game is easy to understand once you start putting numbers into these different tiers. Like in City of Heroes, you could argue that there are typically 1-6 players in pitched immediacy, the same for critical, but several thousand for noncritical immediacy due to the shared cityscape. Functionally, that "several thousand" is more like 80 or so due to the way the city is constructed and the way the servers are sharded.
Those are my suggestions. Let me know what your thoughts are.