In my mind boomer shooter is more doom, blood, and quake, while UT and halo started the genre of more modernish arena shooters (though quake is probably more like a stepping stone between boomer and arena shooters so I consider it kind of both). and yeah the people who played those games in the early to mid 90s are at the very least in their mid 30s right now which is definitely boomer age by current internet definition of the word (nobody can ever even agree what age is technically what generation). Hell im in my early 20s and pretty sure kids born in 2010s would call me a boomer.
Also I really miss how most people would like trim the settings right the way down for the best performance, and the funky little twist in your bunny hops to get to the front line.