This whole issue has me conflicted... I kinda hate both sides on that story so I'm not sure I'd be willing to defend either of them.
Nintendo is free to do what they want on Youtube of course, but I think this is another instance of Nintendo not understanding how the internet works. Most if not all of the big Western publushers are moving towards being more open to Youtubers, and I generally trust those more than Nintendo when it comes to this kind of stuff.
The thing that gets me with Nintendo's approach is that they're not just taking a cut, they're also essentially demanding every Youtuber who wants to monetize video of their games to go through them first. They reserve the right to deny every video you submit them for more or less any reason, so that's a huge ethical concern. If they had asked that of the press there would've been a huge outcry, and I hope as many Youtubers as possible stop doing Nintendo content because of it. This part of the program has been largely ignored, I've only seen Jeff and Jim Sterling comment on it as hugely problematic.
Running it on your own server doesn't absolve you of breaching copyright, and seeing that let's plays can be cease and desisted I'm still not entirely sure if giantbomb is altering it enough to protected from copyright claims.
Sure. But then they could just stop doing Nintendo content. Pretty easy. I've just never heard of them doing anything like that outside of Youtube, I think they're happy with going after Youtubers.