With the Heavensward expansion for Final Fantasy XIV: A Realm Reborn still a few months away (June 23, dudes.), the main scenario writer Kazutoyo Maehiro had a little bit of fun and released a video reimagining the MMO as a fighting game. Square Enix wants everyone to know that this is just for fun and not a representation of an actual project or future plan, but it looks good enough that I'm sincerely hoping that they're just throwing us a curveball. In fact, I would actually prefer this game over the MMO.
You can check out the video, which pits Yda and Livia against each other at the Castrum Centri, below:
Note that people who really want a fighting game based on the Final Fantasy franchise have the Dissidia franchise as an option, although don't go in expecting the game to be pick up and play.