"How can you make a game and then a story."
Easy! It's how the Legend of Zelda series has always been. The development process has always started with the development of core gameplay mechanics and concepts -- the interactive element(s). Story/cinema/non-interactive stuff can be trashed and re-written during development much more easily than gameplay mechanics. The story element in Nintendo games, I've perceived, is generally used to present the different gameplay elements with some coherency or sense of progression.
Mario64 is another example. It's experience is defined by its gameplay, since there was very little story to take in. A fungus telling you "good job you got blah blah stars!" every once in a while doesn't tell you a whole lot. In any case, fun game. You can easily lose sight of whatever story there was and still enjoy it. Rather than "what will happen next" I become eager to find out "what can I do next". This is similar to the original Legend of Zelda. And let us not forget Miyamoto's explanation of the conceptualization of Pikmin.
On the flip side, Eternal Darkness did a remarkable job of tying the story into the gameplay (or miami vice versa). The gameplay WAS the story, or the other way around. Who cares. Well done. But it had a rediculously long development time. 'Dog' knows how long the story was re-written, how many characters and scenarios were thrown out or transformed, in addition to the task of moving the project from N64 to GCN. But I don't believe the game mechanics changed a whole lot throughout its development from what I remember. Mainly the story went thru near-drastic changes (which would somewhat dictate the level design). A ha. Game first, story second.
WHAT THE HECK AM I TALKING ABOUT
HELP ME SOMEONE
EDIT: oh, and Majora's Mask is another Zelda example of developing gameplay before applying story. It's not an explicity black & white case like F-Zero GX where the game is still intact after removing any story it has, but you see what we're trying to say. Nintendo games don't begin with a story idea, they begin with a gameplay idea. MM was born out of the masks and time-cycling/chronology ideas that were originally intended for Ocarina of Time. Wind Waker is in a similar boat (hah) since its concept of utilizing wind physics was also originally planned for Ocarina. We can see that Ocarina has a couple children, regardless of their stories. AM I ON A TANGENT AGAIN. DAMN YOU SINE AND COSINE.