I'm not sure if there's a word to describe a game like this. Sometimes saying it's your 'main' game at the moment fits, but not always. Games that fit under what I'm talking about would be:
CoD Zombies
Risk of Rain
Deep Rock Galactic
Borderlands
Killing Floor
Gunfire Reborn
Dead by Daylight
Elden Ring Coop
Lethal Company
And to a lesser extent:
Party Games (like 100% OJ or Ultimate Chicken Horse. Although UCH can be competitive. Lethal League might fall into this too)
Fighting Games (I don't know much)
Games with Local Coop/PvP like Samurai Gunn, Binding of Isaac, Project Arrhythmia, Streets of Rage 4, and Streets of Fury
And probably more...
On my wishlist I also have Rabbit and Steel, Crab Champions, Helldivers 2, and a game called KLETKA (not out yet) amongst others. I don't mind niche game recommendations.
Game genres I'm not really into would be RTS, City Builders, and MOBAs off the top of my head.
Videos
Are there free multiplayer PC games?
Are there multiplayer PC games for couples?
What is a multiplayer game?
I’m more of a single player person but I love these games