Mario games (and I mean main-series Mario games, not Paper Mario or Mario RPG or whatever you like) are the kind of games that exist simply for their own sake. It's like a shmup -- the story in most shmups is that aliens are attacking, and you must shoot them all down. The story in Mario games is that the princess has been kidnapped by Bowser, and you must defeat him and rescue her. That's all. The game does not exist in order to tell you a story, it exists in order for you to enjoy the gameplay. In other words, it is a gameplay-driven game, whereas an RPG or a game like Half-Life is a story-driven game.
All games used to be gameplay-driven, even RPGs. I think one of the problems facing a lot of developers these days is that their story-driven games focus too much on the story, and not enough on the gameplay. There is nothing inherently wrong with story-driven games; they are some of the best games around, and yes, even Nintendo makes them (just look at the last three Zelda titles). Still, I've seen far too many games go all-out on the story, but no one gets to enjoy it because the game itself sucks. The best example of this problem is Final Fantasy 8. Engaging story and good direction, but how can you possibly suffer through the endless magic drawing, GF summons, and completely pointless dungeon crawling (you don't even find new equipment!) to find out what happens next?
Someone asked, "Who would play an RPG if it didn't have an engaging story?" The answer is: Everyone who played (and occasionally still plays) Final Fantasy 1. Yes, even Final Fantasy wasn't always story-driven. Neither was Dragon Quest, for that matter -- and guess what the story was? Go on, guess. The princess has been kidnapped. You must rescue the princess and defeat the evil Dragonlord. Sound familiar? :)
I think a good test for any story-driven game would be to remove all the storytelling elements from the game, and see if players are still interested in playing it. If not, then your gameplay isn't good enough. If so, congratulations, put the story back in and sell your game.
