“Boomer shooter” refers to old school FPS/shooters in the sense of boomer = old? Never knew that

I always thought it was because of the more fast paced styles of the older games and emphasis on explosive weapons.

Most people who played Doom / Unreal / Hexen when the games were released were early millenials or tail end “Gen X”. From memory, FPS games weren’t really that popular among people in their 30s and early 40s in the 90s. It was all young kids, teenagers and (I am assuming) university students.