I'm sure I've heard this song before, even though I haven't seen much Final Fantasy gameplay (since I've never owned a console I've never had any of those games).
Where does it come from? (Bonus point for a Youtube link.)
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Some googling about the Chocobo Racing OST brought me to the Final Fantasy Wiki, which contains some YouTube videos with a few tracks from the OST.
One of the tracks happens to be Illusion World, which is the one played in the video.
According to the Wiki, the song is from the final boss battle in Final Fantasy III, where it was called 最後の死闘 (Saigo no Shitō), which is best translated as "Battle to the Death".