I reject your idea that it could allow copyright laundering

It's fine, that doesn't change the legality. Unsure whether a judge would include reasoning like this in their judgement.

My license to play the game allows me to incorporate my gameplay into a new work,

No, you are not freely allowed to create derivative works. You are probably arguing fair use or fair dealing, but Twitch streaming generally wouldn't count (it's not part of the list of exceptions).