Nowadays it's mostly Roblox and Fortnite. I saw some 11yo's socialize the other week. One asked the other hey, do you play fortnight? And they swapped contact info that way.
What's the genre of Roblox / Fortnite? Live service games? It would be interesting to have a separate term for them the way we had for "MMOs".
MMOs were also fun from a technical standpoint. One of my big challenges to myself was to make an MMO. I learned a lot about networking that way. When I was 13 I even ended up on the phone with a local business trying to negotiate a dedicated 10 Mbit link. He correctly told me to just wait, that 10 Mbit won't seem so crucial in a few years.
Then there were the MUDs. I'm not sure if it's correct to call them MUDs, but Gemstone and Underlight spring to mind. Underlight especially was a charming little game where you were expected to roleplay in-character whenever you were online. Meaning, no discussion about the real world. It was very addictive for a socially awkward 6th grader to just vanish into this new world.
I wonder what kind of new genres of games people will be talking about in a couple decades. It's tempting to think there's something like "the MMO" that's yet to be discovered, just like the arena shooter was.