There was a time when "online" told you everything you needed to know about a game because there was really only one type of online game. You knew in picking up an online game that you and some friends would be leveling, looting gear, and slaying dragons. It took a while for developers to notice that online play was actually a thing that could work in more than one particular format.
Nowadays, online games range from traditional MMORPGs like Guild Wars 2 and RIFT to MOBAs like SMITE and League of Legends. There's no clear definition for what an MMO is or isn't because so many games are massive, multiplayer, and online.
Maybe it's time to embrace MMO as a broader term than previously thought.