Let's see... Does Elite: Dangerous qualify as an MMO?
Online: Is part of the game played online, rather than entirely on your own computer? Check. (Much to the disappointment of those who preferred a play offline option.)
Multiplayer: Are more than two players able to play the game simultaneously? Check. (Instancing issues aside.)
Massively: Can the game support more than twelve players online simultaneously ? Check. (I remember when MUDs that passed this threshold were described as being massive. YMMV.

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What this game isn't is a traditional MMORPG. For which I'm eternally grateful. I am indifferent to many of the more traditional elements of MMORPGs.
My online gaming time is frustratingly brief far too frequently, so I don't want a pretty graphical chat engine. I want a game I can play. I have game forums, which I can now participate in even more frequently thanks to the wonders of modern technology, for my socializing.
I dislike guild politics, which all too often becomes a monument to one person's ego. I will cooperate with others spontaneously as opportunities arise, but whenever someone suggests joining a guild, my initial reaction is "never again."
And PVP is all about who has the most time to invest in the game to sharpen their skills, and knowing about the latest
exploit broken game balance meta. The former I no longer have time for, and having time for it when I was younger is the reason I suffer from tendinitis today. The gamey nature of the latter, as opposed to making choices based on the nature of the character I'm playing in the game, is why I've always be BAD at it.