No, Destiny is not an MMO according to Bungie
Destiny’s overall structure will feature social hubs, dynamic environments, and optional missions promising exciting adventure and that does appear to seem like MMO. Bungie however argues Destiny it not a massively multiplayer online game.
“These are living, open worlds with evolving stories, changing time of day…and every one is full of players,” says engineering lead Chris Butcher (who hails from New Zealand, the land of Hobbits.
“Destiny is an always online experience, but it’s not an MMO.”
It’s a persistent world (as explained at Post Game Lobby).
Given there’s MMO subscription fee as there are for some of the other game out there such as War Craft, I guess that’s a good sign that Destiny is not an MMO, at least not a traditional one.