Why is story part of this sub-forum?

Because if story had it's own catagory, it would feel empty because Riot doesn't read it ever. (Talking about the fan-fiction here)

Fan-fiction.

Because the Story and Art of LoL are highly influenced by one another.

Because League used to have story, and they haven't finished taking it away yet (and there's still a tiny sliver of hope they'll decide not to do so after all).