People can and do make a living off of sites like Twitch and Let's Play series on youtube, they get the money directly from the ads. NINTENDO HAS ALREADY TRIED TO FIGHT THIS IN THE PAST. They started trying to copyright claim and push nintendo product ads on these videos, so the actual uploader got no money and they did instead. So they stopped playing their games and they backpedaled on the claims, as they "now understood" or something and just wanted to protect their IP. By, uh, keeping the videos up and getting all the money from other people giving them free advertisment.
People can(and do) throw around claims with this stuff, it usually doesn't work. The law around this stuff is still argued a bunch, but when people are streaming/uploading their own gameplay it's different from a movie. It is always technical new content. The only time action is done is when the main head of it(i.e. Youtube or Twitch) is actually contacted about it, and they take the stuff down asap to avoid legal action in general and then figure it out behind the scenes. So at times videos on youtube do go down for their claims, but later come up because the claim is bullcrap. I've been following things like this for awhile, and from my understanding they can't just single out and say "no, you can't stream this". It doesn't legally hold any merit, they would have to target Twitch in general and stop all of the streams entirely. But it makes sense just with a statement from them that most people would immediately respect and honor it to avoid taking it any farther, which is what evo did at first. They don't file paperwork or anything, that's hilariously off base. Anything like that is handled through the host of the website, not the stream. So, Twitch. And obviously they're legally sorted out, I just fucking watched a Melee stream for a few hours last night.
Nintendo are literally the only people who even seem to care at this point. A single lone soldier fighting a pointless war.