He is using "boomer" figuratively, not implying that he is literally old enough to fit the baby boomer generation, but using the word "boomer" to describe someone holding onto a severely outdated set of beliefs, characteristic of a person that is a part of the baby boomer generation. I believe by "no boomer shit" he is trying to say "it's not like I have an outdated view on technology, but". But says it in a way someone brain-damaged by too much Internet from an early age would.