I think both are in the right on this one. Ninten does have the right to take some of that money from youtubers using footage from their games as they are their games. It can also be a negative with Let's Plays if they show the entirety of one of the games and people watch them rather than buying the game for themselves.
However, with how big video games are on youtube and some of the most popular channels being about video games, this is free advertising for them, as big names like PewDiePie can expose and promote Nintendo's games to a massive audience, build interest the the games, and get more people to buy the games, netting them more potential buyers.
While it's understandable that Ninten would have a piece of the profit and may be somewhat against their games being posted on youtube, there is a lot that could be gained by giving these youtubers more freedom to use their content however they see fit.
Dance my pretties!
The Official Art Thread - The Official Manga Thread - The Official Starbound Thread
