There's absolutely no way anyone can realistically claim an LP isn't a 'derivative work' under copyright. As such, the game's maker -could- have the videos pulled and sue their ass into oblivion.
LPs contain far too much footage of the games in question to count as fair use. A couple of minutes in a review is fine; hours and hours of start to finish video is not.
The amount of footage isn't really relevant here. It's patently ridiculous to argue that a video recording of someone playing a game is anything remotely close to the experience of playing that game (i.e. the LP videos are not the game itself). A video recording of a movie is that movie, but a video recording of a game is not the game. Therefore it's not at all clear that a LP video would not be fair use, since the presentation is highly transformative (since the experience of playing the game and watching someone else play it are completely 100% different). To quote Judge Pierre N. Leval (as used by the SCOTUS in their explanation of fair use):
The use must be productive and must employ the quoted matter in a different manner or for a different purpose from the original.
I would say that LP videos fit that understanding exactly. Standard disclaimer: IANAL.
Oh, and this is incredibly and unarguably a stupid decision on Nintendo's part. That much is certain.