Hi ,
A think a distinction should be made here.
A Co-op, with smaller groups of players connecting through a lobby, but only a limited number of players existing in a given space, would actually be considered a Multiplayer Online Game (MOG) – nix the extra “M”. The “massively” part comes into play when hundreds+ of players exist together in the same space. This is why you don’t hear games like Call of Duty or League of Legends referred to as MMOs. Publishers understand that (incorrectly) attaching the “MMO” tag to these games would confuse much of their regular player base (and be somewhat misleading to first time players).
I hope that helps.
Cheers,
-D