Wow, it looks like you basically never paid attention during lectures then. Fantasy isn't a sub-genre of Sci-Fi. They sit beside each other in what we call Speculative fiction.
Also, mythology and magic are popular themes of Fantasy, they do not completely make up Fantasy. It doesn't need to be medieval with wizards and magic in order for it to be considered Fantasy.
FFVII is not Sci-Fi, it's steampunk, which is a sub-genre of Fantasy and Speculative fiction, not Sci-Fi.