They have to defend their trademark. They don’t have to defend copyright, and most of Nintendo’s reputation comes from copyright claims. Someone streaming a let’s play isn’t selling a counterfeit Mario game, they’re just showing you things in a real Mario game, so there’s no trademark claim.

They’re also big abusers of the fact that most of the people they make copyright claims against can’t afford to defend themselves against such a behemoth. Even if you’re sure you’ve not violated their copyright and your lawyer’s sure, too, it’ll be much cheaper to roll over than get the legal system to agree with you.