A strict definition is hard. The first thing that came to my mind was 'like quake'.

Fps games have come in phases. Most recently looter shooters, before that battle royals, before that hero shooters. And quite early in that chain you had boomer shooters.

Fixed pov would certainly be a step down that path but I wouldn't call it a requirement. If Quake got a faithful remake with all the advancements of 2024 and non of the industry trends that'd be a boomer shooter.

If you made a brand new arena shooter with no classes and an array of ~8 distinct weapons (think one rocketlauncher, one SMG, one pistol etc.) laid across the map focused on something like TDM or KotH, that could be a boomer shooter.

It's kind of like porn, you know it when you see it.