Dang, my perspective on this went on a roller-coaster as I read the posts.
First confused as to the existence of "boomer shooter" in general, then thinking it was about explosions, then the notion that it's a reference to Baby Boomers? I mean, my dad was a fairly young Baby Boomer, and he had zero interest in FPS's. Which is anecdotal, I know, but I really think 2.5D/3D gaming was primarily the purview of Gen X.
I'm just a handful of years away from being lumped into "Millennial", but I still have very clear memories of the release of Wolfenstein3D, Doom, Quake, Heretic, etc. And most of the programmers were fairly young (though older than me.) Heck, I was programming (mediocre) text adventures when I was 14-18. (By the time I was 19 the genre was seemingly dead and buried, only to resurrect several years later under the name Interactive Fiction. Or maybe it was always there and I just didn't know where to look. But I digress.)
If I were going to assign a label to any games as "Boomer," it would be the early arcade games (Galaga, Donkey Kong, Pac-Man, Asteroids), pinball, and text adventures. And Solitaire.