Wouldn't it be funny if they made her play the game first so she can write the song for it? Kind of like how artists usually get to view movies before they start on its theme song, you know? Hahaha.
Nah, but seriously, it's most likely a new single written for the game; whether it'll be her leading track or coupling track is a totally different story, but I think it's highly likely it'll be a new track. The only recut track (correct me if I'm wrong) is Secret for that Chinese movie (which I'm assuming was recut on budget restraints). I'm not entirely sure on Depend on you's situation, but I'm pretty sure Startin' was written for Onimusha or at least inspired by it. Then we also have HEAVEN and Rule, both written for the movies SHINOBI and DBZ.
I only really recognize GIRL NEXT DOOR's track, but that alone makes me excited to see if maybe it'll be like a lead single for Ayu's trance album.