Plenty of Nintendo games have a fairly deep narrative.
Hyrule Warriors, pretty much all recent Zelda console games, Bayonetta, Xenoblade, Kid Icarus Uprising, hell even Metroid have a storyline/cinematics all over the place.
So it's not like Miyamoto speaks for all of Nintendo.
But I understand what Miyamoto is saying, he's saying the game designer should approach game development with the idea that they are making a game ... not some "head in the clouds" concept of "I've always wanted to make a Hollywood movie, so I'll make that and just squeeze a game in around it".