What is the name of this classical music piece
The amount of interesting stuff from Russia on the Internet is large enough that it pays learning the cyrillic alphabet.
M. de Falya Ritualniij tanets ognya iz baleta "Lyubov-Volshebnitsa"
So the title would seem to be some "Ritual" from the named ballet by Falya.
Googling finds "Manuel de Falla" and with regard to ballets and rituals I find in his Wikipedia entry "The ballet El amor brujo ("The Bewitched Love", 1915) which includes the much excerpted and arranged Ritual Fire Dance ("Danza Ritual Del Fuego")".
"Danza" seems to be related to "tanets" so that is my best bet from just milking the cyrillic alphabet.
Here's another orchestra performing the same piece; the video is labelled as the "Ritual Fire Dance" by de Falla, as you suspected.
Yup, and there's also a piano version from Falla himself. I rather prefer the piano version and played a lot faster than on the video in the original question. This performance https://www.youtube.com/watch?v=EmZC2WjU-Fw is quite to my taste.
To contribute to your analysis of the Russian: ognya might be a distant relative of the Latin “ignis” – fire.