The videos in question are people showing what can be done with something which is copyrighted. They videos don't provide any ability to play the game. The games are only being played by a single person. There is no copy of the game being made.
A running commentary of a single played instance of a game is entirely different than sitting down with a controller in your hand and playing the game. That seems significantly transformative to me.
And that's a huge problem with copyright law, it's so grey in so many areas. If the exact situation hasn't been defended in court, it's unclear whether or nothing something is legal.
What if it isn't a RPG? What if we're talking about a video of mario kart?
If I bought a physical Nintendo chess set, I don't think anyone would claim a video of my gameplay would be Nintendo's property. By extension, a video of me playing a virtual nintendo chess game with my commentary should still be mine, after all, the story is being written by the players. I think that's fairly analogous to a commentary of a mario kart game.
Now it gets interesting with a role playing game like zelda perhaps. I certainly have a right to produce a gameplay from it. Do I have a right to record it? Why not? How is it really any different that recording a play with a physical object, something which is done every day. Nintendo may have the storyline, but they didn't create the actual play. That is a result of an authorized use of the game. Player runs over here, picks up a sword -- that's something the player did, not Nintendo.
I think in the end it boils down to what the lawyers can convince a judge is true, rather than what can be proven or what is the law.
Song mashups already go from songs to similar-sounding songs and those are fine. Again, IANAL, but if mashups are okay, it makes sense to me that Let's Play videos should fall under the same - if not more generous - rules.