English, too! I love Fr. Aju Philip Matthew's voice! Here is another clip of him celebrating the Qurbana in English, with a little bit of Syriac: http://www.youtube.com/watch?v=yWChywFF9eQ
I am not Syriac Orthodox, but in the book "Queen of the Sacraments: A Treatise on the Liturgy of the Holy Mass as celebrated in the Syrian Orthodox Church" by Fr. Mani Rajan (2008, Travancore Syriac Orthodox Publishers), prayers of thanksgiving are listed as occurring after communion, so I would guess it is some of those. We give thanks to Thee, O Lord, for the abundance of Thy mercy by which Thou has accounted us worthy to partake of Thy heavenly table. Grant, my Lord that our participation in Thy Holy sacraments be not a cause of our condemnation and that being accounted worthy to partake of Thy Holy spirit we may find a share and an inheritance with all the righteous forever. We offer up glory and praise to Thee and to Thy Only-begotten Son and to Thy Holy Spirit forever.
(p. 163, "The Conclusion")
The little bit of English in the video does not match up with this, but this is an example of the thanksgiving prayers said at the conclusion of the liturgy, according to the book. Hopefully a member of this church can give a more definitive answer.