Fan Fiction: ALL storygames based on or inspired by other properties belong here. - it is a bad category definition.
A storygame that accurately follows an existing book/movie/etc. is not a fiction made by a fan and may have another category. An example is your own story "The Firebird, a Edutainment by Sethaniel".
"or inspired" - it's ok to be inspired by other story as long as it does not explicitly use the same world or characters.
From wikipedia: fan fiction is fiction about characters or settings from an original work of fiction, created by fans of that work rather than by its creator.
I propose a more accurate category definition: ALL storygames about characters or settings from another work of fiction whose plot differs from the original belong here.
(or use the one from wikipedia)