If there’s copyrighted material posted on a different platform that’s not uploaded by the copyright holder, I can share a link to the material without being sued because I’m not the one violating copyright laws. I can share a scene of a movie I found on YouTube that’s uploaded by some random person without permission and we could all watch it before the video gets taken down.
If the goal was to drive traffic away from Ethan’s channel, his streams would have to be uploaded elsewhere without his approval. He’s suing the moderators who uploaded his content to different platforms, not the users who shared them.
I’ve seen some of his detractors calling it an attempt to stifle free speech and criticisms against him, but at the same time, the system around reaction content is broken, where YouTubers can upload other people’s content, provide meaningless commentary (if any) and call it “fair use”.