The Circassian text goes like this:
Batsä ts1yk1w zish1wrä, shabäts1yk1w qofä
Batsä ts1yk1w zish1wrä, zighäsh1aghw qofä
Batsä ts1yk1w zish1wrä, daxäts1yk1w qofä
Batsä ts1yk1wr, qofär wey
In the original Cyrillic:
Бацэ цIыкIу зищIурэ, щабэцIыкIу къофэ
Бацэ цIыкIу зищIурэ, зигъэщIагъу къофэ
Бацэ цIыкIу зищIурэ, дахэцIыкIу къофэ
Бацэ цIыкIур, къофэр уей!
God knows what it actually means, though. The "oi-da-ri-da-rai-da" type stuff is just vocables.
The original Circassian song is this, by the way:
https://www.youtube.com/watch?v=m2y08gVeJHs
I found YouTube links in your post. Here are links to the same videos on alternative frontends that protect your privacy:
Link 1:
Link 2: