I'm suprised by how people don't understand what he's saying. He isn't completely disregarding story or narrative, what he's trying to get across is that a game shouldn't be made with story as the driving force. The gameplay should what makes you want to play it, can their be a story, of course there can he didn't say there couldn't but if you use gameplay just as means to get to the next part of the story that's a problem.
I'll compare Ocarina of time against Assaisians Creed 3, just as an EXAMPLE. If you took the story out of Ocarina of time you still have a decent game with a puzzle solving combat style of gameplay, and a open world to explore. If you did the same to Assasian's Creed 3 I'd say it suffer more heavily since I often felt the combat and stealth were lacking.(though some may still enjoy it without the story).
Story is important in games I enjoy it myself, but gameplay and design is what's going to make me play the game again, it's what makes the expierence hat Miyamoto was talking about here.