Leaving Pokemon and several Mario games aside:
I'd like to take what Miyamoto is saying in another direction. He believes the experience of a game should be the focal point. He finds that the story by itself would be boring without the experience to back it up. However, a narrative is a bit different. TLOU for instance has an engaging narrative, but regarding a good number of the best films, they don't require that. Many of the best films focus more on the dialogue, acting and character development and leave an intertwining narrative aside.
For video games, an engaging narrative is almost completely essential in order for a story to work well because you are playing a video game. You want to be able to travel to different places and experience a variety of things happening.
Resevoir dogs for instance really only takes place in one area though with flashbacks happening, so the narrative isn't all that and a bag of chips. The dialogue, characters and spots in the movie are extremely entertaining though.
If a video game only took place in a single area throughout the entire game, chances are it would be boring. And if a game puts all of what it offers only into story, but without an overarching narrative to progress it, then it would also be boring.
If it also has good gameplay, then good for it. However, unless the gameplay is incredibly engaging, taking away the narrative even with good dialogue and character development would be fatal to the level it once was.
Lube Me Up