???
"Coils of Light" in this album is in English, and isn't sung by Raychell (see credits on the album page).
The single I linked, and the youtube link you posted, is the version sung by Raychell (not in this album).
Which apparently isn't used in the Japanese game and was just for promotion (due to some copyright problems?), ex:
https://www.youtube.com/watch?v=nXS3o62QFLE