This is digital music from RPGs not Square-Enix. Digital music can come in a variety of forms, .it, .s3m, .mod, and .xm. If the song is made well, it can sound better than midi! The only drawback is that sometimes they can get a little large, but not as large as mp3 files. There is one great freeware digital music player: ModPlug.
In each file type of music, you can either download the zip file or seperately.