It definitely isn't a MMO in the traditional sense, which was defined by WoW. On the other hand WoW wasn't the first MMO either so there is no reason the term can't be redefined.
Elite is a MMO because hundred thousands of players affect and shape the same galaxy.
I love how people throw WoW out there and call it "defining". Fact of the matter is that WoW was on the heels of the real defining MMO, EverQuest. However, EQ was not the first, nor the second, it was third with Meridian 59 being first and Ultima Online being second. EQ did however, "define" what MMO was.
MMO (Massively Multiplayer Online) is pretty easy to define, It is a game that has a persistent world that can support more than 64 players online simultaneously on the centralized game server/farm where players can interact with each other.
ED has a persistent world.
ED supports more than 64 players connected to Frontiers world servers.
ED is played only through a networked connection to the world servers.
ED players can interact with each other by chance or purposely.
By all accounts, ED is an MMO, it may even be considered as an MMORPG, since the player is role playing the CMDR out flying their ship and doing what ever business they feel like doing in the persistent world.
It doesn't get any more simple than that. And all you armchair developers out there that are going to try and argue your own definition of what an MMO is, don't bother, I helped define what the term MMO means back in the late 90s, I know what an MMO is.