If I buy a game I've paid the price of admission. The developer doesn't own the rights to me playing the game in my living room and if I film that then that's mine. It's a piece of software. if I film myself typing up a novel and the novel goes on to become the next Hunger Game sensation and the videos do billions on Youtube I don't owe Microsoft any extra money because I used their software in the videos because I already paid Microsoft for the software.
These developers are salty because someone has figured out how to generate revenue through a loophole using their software. They want that extra revenue too but if they attempt to capture that revenue stream it would cease to exist. The same developers aren't paying the cost to create those Youtube videos. They don't buy the console, the capture equipment, or computers involved. They just see somebody else making a buck and feel entitled to it.