Im gona assume by your post that you are either in your 30s+ or not keen on social media.
The triggered feminist is a meme that comes from tumblr, it comes from people in that platform complaining about everything and actively asking trigger warnings for the most mundane thing.
Example
http://i.imgur.com/3MdC2vA.jpg
Like most people on the internet, you are trying to analize a situation without context.
Ethan has an audience, most of them are aware what a triggered feminist means, it is in fact a mockery of someone who the internet would clasify as a extremist feminist, not all of feminist.
It is not his fault you are not into the jargon that is used in his community, the same way you are not expected to know what "repping the nash" or "papa bless" if you dont follow the circles in which he does jokes about. Now granted, the two examples are jokes he started but in general everything he does is related to meme culture and the "crazy feminist" is a meme as well.
I think you just need to understand that terms are used differently in different places on the internet and some communities use their own jargon and like you do, separate what is said on a video in the internet adressing people on the internet to what people say in real life.
He is in fact not using the terms incorrectly, hes using them correctly to his audience.