If it's their content, they can take it down. Shitty, but that's the way it is. Fair Use is a doctrine that is mainly for U.S. with some similar legislation around the world. In many EU countries Fair Use doesn't exist as such. YouTube videos are global and can be subject to hundreds of different laws. If looking at it from purely U.S. point of view there are 4 questions that must be looked as per the legislation:
- the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
- the nature of the copyrighted work;
- the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
- the effect of the use upon the potential market for or value of the copyrighted work.
Now this kind of videos would need to be taken to a court to get a definitive view, but if the video is monetized, it's more than likely it's not fair use. The second question in these cases would be irrelevant and in this case the third point, the use of copyrighted work is limited. Nintendo could argue in courts that showing how to circumvent the copyright protection of their devices would affect negatively their ability to exploit their own market. While Homebrew is perfectly legal and a great thing, the side effect is that some bad eggs use the homebrew community to enable pirate copies of games. Leaving works like this online could therefore potentially harm Nintendo's ability to exploit their own market. The burden of proof lies on Nintendo though.
In summarum; Fair Use doctrine is not clearly cut for either way. The copyright laws around the world include anti-circumvention laws so those might be taken into consideration as well.
Note: I am a Civil Law lawyer, not Common Law lawyer, so any U.S. lawyer can correct me on this.
Shame though, as homebrew usually enables great things.