I think it's better to view media as a multi-dimensional spectrum - interactivity, story, audio etc. can all make their own valid contributions to the quality of the end product, and there can be variable emphasis on each - that is, our definition of 'game' is too narrow, and only really focuses on one of many factors which contribute to the end product. For example I've already raised Dreamfall, which has a brilliant storyline, and where it was praised by some critics, others panned it for the minimal level of actual gameplay involved - at parts, it was more an interactive movie than anything else.
That is, you can have a bloody good game which relies primarily on one aspect of the medium other than interactivity (though in the process you may be blurring the definition of 'game') , and equally (and in my opinion, ideally) you can have games in which there is interplay between these aspects - i.e. they rely on eachother: for example, in the case of Phoenix Wright (and most adventure games), the gameplay is the storyline (in that your actions directly contribute to its progression, and the 'aim' is essentially to progress the storyline), whereas in Mario the storyline is simply a premise for why everything is going on.
EDIT: This is where I hope that makes sense to anyone other than me.
EDIT 2: Xocrates - that's essentially what I was trying to say in my OP in this thread re the example of Ocarina.