Excellent answer from Angst! On an harmonic perspective, the piece inquired about is also far from renaissance music, which tends to be somewhat static or obey to basic tonal progressions.
The piece inquired about uses a descending progression sometimes called Andaluzian progression for its reminiscence of that kind of music, but that's been used (battered, I should say) in modern times in many many pieces and that's exemplified in this video:
One of my favourite examples of the usage of this same progression is from Rick Wakeman's 1973 album the Six Wifes of Henry VIII, in the beginning of this track:
Funny, the subject of this album is also about a renaissance character, but's just a coincidence.