I see. I dont think it is very common, but i know it did exist for quite a while since some traditional brazilian songs also use the same style of singing.
It reminds me a little of arabic, so maybe it has something to do with muslims culture, considering that both Portugal and the Caucasus suffered influence from it? The only problem i see with this is that Galicia suffered a very brief occupation by the moors (720 - 729) so the cultural influence there isnt that big.
About the "traditional" music you posted, it sounds like a bad tatar music, not russian. Some soviet war songs like poljushko polje out of the top of my head, are very pleasant although they dont really fit in the folk or neofolk description. It really is a shame that the soviets destroyed much of the russian culture, but oh well, jews gonna jew.