I don’t think an arena shooter necessarily has to be multiplayer (but they’re mostly only fun when they are)… but it heavily implies that the maps are… arenas. Smaller areas that you backtrack through constantly with no “end”. Matches probably end by a condition like a timer or kill count or something. That said, I think we use “arena shooter” to distinguish games like Quake 3 from CoD (with some differences like weapons being on the map and players spawning with the same barebones kit)… but arguably CoD isn’t that far removed from something like Quake 3 (which I know is heresy and they play very differently, but the fundamentals aren’t so different).

Arena shooter is descriptive of certain mechanics. Armor/weapons with tinted spawns on the map, usually some kind of bunny hopping, but that's not mandatory, and often portals/verticality.

I'm talking about quake, unreal, warsow, xonotic, etc...

I think what you guys are on about are games like doom, Wolfenstein, Duke nukem and so on. Not so much quake but single player.