I think any massive online only game is considered an MMO.
I used to think the same as you, but I realized I was wrong one day. I read about MMOFPS somewhere (probably Game Informer, I don't remember), and it turns out the games such as Combat Arms (meaning round based games) are
not MMO's.
What makes an MMO an MMO is a persistent world, the opposite of round based. Check out this Wiki article that is exactly right.
"MMOFPS is an online gaming genre which features a persistent world and a large number of simultaneous players in a first-person shooter fashion.[12][13] These games provide large-scale, sometimes team-based combat. The addition of persistence in the game world means that these games add elements typically found in RPGs, such as experience points.[citation needed] However, MMOFPS games emphasize player skill more than player statistics, as no number of in-game bonuses will compensate for a player's inability to aim and think tactically.[14]
Wiki List of MMOFPS Games
10SIX (now known as Project Visitor)
World War II Online
Neocron
PlanetSide
Upcoming
Global Agenda
MAG: Massive Action Game
Huxley
I believe games such as Combat Arms are referred to as Online FPS or Online Shooters. The genre of MMOFPS is different.