People play Nintendo games for the game mechanics, not the story. Zelda and Mario are both about rescuing the Princess and defeating Bowser/Ganon. That's the Alpha and Omega of the story. Some details might differ, the exact how and why might differ, but its the same.

But the reason it works is because when Nintendo releases a new Mario or Zelda game, they also change the way it is played, introducing new challenges, dungeons, puzzles, and mechanics throughout the game, and they tend to do this part really really well even if the cast of characters is largely the same from game to game.

Sometimes that isn't the case, the NSMB series really could just disappear and nobody would care at this point, but that doesn't mean Nintendo can't introduce original ideas.

Yahtzee, for his part, cares mainly about two things. Is the story good and is the game fun? The story doesn't always have to be groundbreaking for him to be having fun, but it is a lot more fun for him if it is a good story because oftentimes, that's all he really wants and a lot of the things that make games fun for other people, don't necessarily do it for him. Saving the Princess over and over again also just doesn't do it for him, and I can respect that, but when the writing is really good, he can even enjoy that part of a Mario game. Just check out his Paper Mario: The Thousand Year Door review.