Firstly, I know that Nintendo lagally can do this. Under current law.
One thing to realize is most of the industry is for letting youtubers profit from making videos of their games. Microsoft is for it, as well as minecraft (I know microsoft bought out Mojang, but they were for it before then.) Lot of indie developers allow it, because they realize it creates a lot of ad revenue. Many of them would have never been noticed if there wasn't videos being made about them, getting people's eyes on them.
Nintendo's is also flagging reviews of their games for getting revenue, like what's already been said for Angry Joe. Critical analysis of products is protected. Why wouldn't it be, as it would create a weird situation where someone could put up any product they wanted, no matter how bad, and other people couldn't review it, informing the public before they make a purchase. I repeat. Nintendo legally owns footage of their own game, but they can not own someone else's critical analysis of their work. That is protected under free speech, and this is Nintendo stepping out of their bounds.
There's been cases of Nintendo flagging hour long talk discussion videos, because they showed a 30 second trailer of one of their games in it, taking all the revenue from the entire video.
Now, one thing, Nintendo has no right to take all the revenue for a video when the part that pertains to them is only a small fraction of the total video. This is them stepping out of their bounds for sure. Taking revenue that doesn't even legally belong to them, as it's not even pertaining to them.
Second, they are flagging videos for showing trailers. Promotional material. Specially made footage that the company wants as many people to see as possible. How can they take revenue when the video maker is essentially showing an ad for a Nintendo game? That's really what a trailer is. An advertizement. This is promotional material that Nintendo sends out to media outlets, telling them to spread the word about their games. How can anyone be incentivized to put up videos, that are really advertizing for Nintendo, when they will get nothing out of it. Nintendo will flag it, and take the money for themselves.
Nintendo can do this legally, yes, but there's been many cases of them stepping out of bounds, and taking revenue that doesn't even legally belong to them, because the flagging process of videos is so out-dated and archaic.
I hope Nintendo realizes that by doing this, they are going to have to do all of the advertizing for their games themselves. They are already starting to do this, as evidenced by their "Nintendo Directs" they've been doing, instead of taking the traditional media outlet route sometimes. It's really sad that Nintendo is preventing many of it's fans from being able to profit by spreading the word about them. You have Angry Joe, PewDiePie (The biggest youtuber there is right now), Total biscuit, and many others boycotting Nintendo. Refusing to make any more video's about them, or even wanting to talk about them anymore. You get too many people not even willing to talk about you anymore, it's really going to start hurting your sales (Which their sales have been pretty horrible the past few years, honestly. I know they've made many other mistakes with the 3DS and the Wii U, but this revenue taking is a part of it.)
Just my two cents.