What makes an arena shooter? To my knowledge and experience, the term "arena shooter" started being used in the 2000s to retroactively distinguish the fast, fluid, skill-based deathmatch style of FPS gameplay from what was becoming nuovo; the slower, ADS, sprint lowering your weapon, kind of gameplay.
If it's indeed just the gameplay style of the multiplayer that earns the label "arena shooter", then doesn't that mean that Doom, Duke 3D, and other early deathmatch multiplayer components arena shooters? Does it matter if there's a single-player component or not? People always refer to Quake 3 as an arena shooter, which didn't have a robust single-player component, but why are Quake II and Quake for example not the first thing that pops into your mind when you think "arena shooter"?
Finally, how important of an distinguisher is team-based gameplay vs. deathmatching? Is only deathmatching allowed in arena shooters, or is something like Quake 3 Team Arena also an arena shooter due to it sharing the same general movement and combat design as Q3A?
Maybe it's not just the movement and combat, but also the enclosed and tight arena-like maps as well that enforce the fragging to never stop.

I've just never liked the term because it's never been very clear, or maybe it is clear and a lot of people just use it, maybe not wrongly, but haphazardly. I want to see what people think.