Continuing gaming's long tradition of dumb names for game genres, boomer shooters are first person shooters that don't use auto-regen health (COD, Halo), in offline they give health frequently from killing enemies (rather exclusively health packs), and they're designed to be fast paced, usually with a wide FOV, an absurdly high "walk" speed with no run button, and somewhat disorienting or labyrinth-like map style. They're often offline, but can be multiplayer player-vs-player.

Even if the game is completely modern: Doom Eternal, Ultrakill, Dusk, Turbo Overkill, etc its still called a boomer shooter.