I wasn’t even aware that it was an MMO.

The entire galaxy is shared by everyone playing the game, in real time. You can encounter each other, fight, team up, or avoid each other, and your actions influence the state of the shared simulation. Definitely an MMO.

What am I missing?

The most recent thing you probably missed was the thargoid war, and (very recently) the battle with the titan that parked itself over Earth and took over the Sol system. You might compare it to a fantasy MMO raid, but at a much larger scale.