Massively multi-player (online) aka MMO, is a classification for a game in which all or most portions of a game allow for frequent and random encounters between the player and other online players. More refers to the PvE side, as PvP necessitates other players regardless.

I love this game but it's not an MMO. In real MMOs your player encounter can be up to 100's. The max you have ever seen in Destiny is 12. And that's in the tower or pvp. Raids in MMOs are a lot more than 6 players too. This game has MMO elements but it's not an mmo. Nothing massively multiplayer about it. Not knocking the game just making a point.