Fans of everything that Square Enix does should be on the look out for Gyromancer, a trademark recently filed by Square Enix for use in services such as "computer game software" and "video game software."
That's typically a good sign that Square Enix will use Gyromancer for a computer game or video game. We'd go far enough to call it "likely." Will it be an all-new franchise? Maybe. Square Enix is often a little more loose with its WiiWare and iPhone app releases when it comes to trademarks, so don't be surprised if this string shows up on the digital distribution platform of your preference.
Plan instead to be a little more surprised if the game has the massive production values of a Final Fantasy or Dragon Quest title.
Our best guess is that Gyromancer will be a game about R.O.B. finding love at a Greek fast food restaurant, with RPG elements. Hey, we don't have a lot to go on.