Honestly, when I first heard the term “boomer shooter” I thought the games were called that because of the amount of explosions they have. Ion Fury in particular is full of them. It a was a while after I realised that by “boomer” they basically mean “old”.
I think “retro shooter” is the much better term, though “classic” also works.
When I was a teenager in the 90s I played doom with both friends of my age and of my parents generation. They would have been in their 40s but not really “old”.
Looking at the maths boomers would have been between 30 and 48 when doom became widely available in '94.