Excellent answer from Angst!
On an harmonic perspective, the piece inquired about is also far from typical 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 flamenco music. There are a few notable examples of the Andalusian progression in music from the renaissance, but they are isolated cases, not typical of the music of the era.
For those who care, the progression can be seen as part of the Phrygian mode, and modal harmony was sometimes used in renaissance music, as opposed to the classical or romantic periods.
Jazz music is the main responsible for the more generalized use of modal harmony in modern music, but the use has been generalized to all genres of music, so nowadays in you can find examples of chord progressions outside of the more common major and minor tonalities in rock, pop, classical and, perhaps especially in film and game music, as the use of modal harmony helps to establish specific moods and enviroments.
This type of progression, explained in this video, has been used (battered, I should say) in many many pieces.
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 the track "Catherine Parr", although the progression here used is only the first 3 chord of the "andaluzian" progression.
Funny, the subject of this album is also about a renaissance character, but unless the composer of Assassins Creed was inspired by the album, that's just a coincidence.