It's called Final Fantasy Dimensions, and it will be out for iOS and Android in coming months. Looks like Final Fantasy IV or Final Fantasy V, no? It's not; it's a nostalgia-themed original game with touchscreen controls and some seriously classic gameplay.
It was also released in Japan two years ago under the name Final Fantasy Legends. (Not to be confused with Final Fantasy Legend, which is the US version of something that isn't a Final Fantasy game at all, but let's not get into that right now.)
Classic role-playing games seem to work really well on touchscreens, as evidenced by the success of Square Enix's ports and indies like Dragon Fantasy, so I'm looking forward to this one. Check out the video above, as shot on the show floor during E3 this week, to see the whole thing in all of its old-school glory.