The video was actually mislabeled, this is actually the first part of Psalm 51 (or 50 or 53 depending on translation):Musical Aramaic rendition of the Our Father:
Have mercy on me, God, in accord with your merciful love; in your abundant compassion blot out my transgressions.
Thoroughly wash away my guilt;and from my sin cleanse me.
For I know my transgressions; my sin is always before me.
Against you, you alone have I sinned; I have done what is evil in your eyes
So that you are just in your word, and without reproach in your judgment.
Behold, I was born in guilt, in sin my mother conceived me.
That's Fr. Seraphim chanting it, he has a CD "Chanting in the Language of Christ" which I strongly recommend. Note though that the Lord's Prayer in it (Baban D'Bishmaya) is in Assyrian, which I understand is more modern.
Here is "Our Father, Who art in Heaven" in Syriac (Abun D'Bashmayo):