A game is called a boomer shooter based on several criteria. Usually they’re first person. Does that mean a third person shooter can’t be a “boomer shooter”? No.
Quake III is just one game that boomer shooters are based on. Doom (1993) is a game that boomer shooters are based on too. Neither one is a boomer shooter itself. A Boomer Shooter is a modern creation meant to replicate past play style, video style, and audio style too… It’s more than just “pixelated/voxelated…”