I don't think it's right.
The line between a crappy Lets Play and one where the creator adds a significant voice and style to their video are too narrow in a legal sense. I feel like there are plenty of Youtubers that produce content with enough skill and style that the game being played isn't the main draw and it leans more into creative and artistic expression based around the video games world. I can argue that many people use the game to create an extremely unique product. Sure, they're using a game created by Nintendo but how different is that from a guitarist making money off the music he creates with his Les Paul or Andy Warhol selling a painting of a Campbells Soup can? That may be a stretch but if someone is expressing themselves through their lets play videos and puts in significant amounts of time to learn the craft and find their voice and how their voice fits in with the game being played I don't see how it is different than any other instrument.
I think unique content, even art, can be created within the confines of a game and if the Lets Play producer is creative enough they have every right to monetize what they make.
Maybe this is actually a good way to give youtubers (worst word ever) the incentive to create better content that is more in line with their personality and less focused on the game being played. If we want to make the argument that games are art than we can't look past the fact that they are also interactive experiences. All the humor, love and meaning that the creators of the game inserted into the experience can be molded by the players to make it unique to them.
At the very least the lets play creators should be given some of the profits for the hard work they put into their creation. If Nintendo is able to make money off of something that they didn't post or make then so should the Youtuber.