Interesting. I am ashamed to admit that Indian Christianity is not something that I know very much about, despite that fact that we in the Coptic Church are in communion with millions of Indian Orthodox around the world. I don't really like the instrumentation that is in the video you've linked, but it seems from Youtube videos that even the Orthodox in India often use instruments in the liturgy, too (though maybe less than the Catholics? I don't know). But there is still plenty of traditional chanting, thanks be to God:
Hymn for ordination to the priesthood, in Syriac, Malayalam, and English
Syriac chanting lessons at Malankara Syriac Orthodox Theological Seminary
Prayers at Kottayam Orthodox Theological Seminary
Malankara Orthodox liturgical song "Orthodukso vishwasam"
(note the tone/ison-like arrangement borrowed from the EO, even though there isn't really much of an EO presence in India!)
Translated text of the song in the last link (with thanks to the internet, as I don't speak Malayalam):
Come let us celebrate the remembrance of our holy fathers who gave the true orthodox belief to the world.
We remember Ignatius the Fiery One and Theologos (I think this is St. Gregory the Theologian) the sea of wisdom.
Kyrillos the sweet waterfall and Ivanios the Golden Tongued ( = St. John Chrysostom).
We also remember Baselios and our master Gregorios (of Nyssa?)
as well as Dioscoros, Clemis,
Philexinos and our illustrious Severus.
May God help us with their prayers.
And from the Malankara Catholics (not Orthodox), I am in love with this particular liturgical fragment
...what a voice Fr. Aji has! I suppose Fr. Aju Philip Matthews Kashisho
is our equivalent in the diaspora.
(i.e., the one video I cannot post on Indian Christianity without including...heh.)