They are not Russians there, there are tribes with other genetic makeup. They have 50 centuries for 2,5 million of population in Dagestan Republic for example.
Even NY Times has an article about longevity there.
Why They Live to Be 100, Or Even Older, in Abkhasia
Thanks for giving a bit more info about it.
I did a quick google. That article is from the 70s.
This article from 2018 describes the diet quite differently than you do though:
In addition to uniquely active lifestyles, the Abkhasia are also known to follow a mostly plant-based diet, emphasizing fresh (as in "picked-it-this-morning" fresh) foods, whole grains, and nuts. The day typically starts with a fresh salad of raw greens harvested from the garden. Nuts are served at nearly every meal, bringing in antioxidant value, and they are known for their matzoni, a cultured milk drink. But perhaps just as important as what the Abkhasian people eat is what they do not eat. They are a community that doesn't consume refined flour, oils, or sugars.
Not only are the Abkhasia known for the fresh foods they consume, but also their overall caloric intake. The average Abkhasian diet contains well below the prescribed 2000 calories per day. The Abkhasia not only eat wholesome foods but comparatively do not eat very much of them, which is not much of a surprise for many longevity researchers as limiting caloric intake has been shown to increase life expectancy in laboratory situations.
What We Can Learn From the Remarkable Long-Living People of Abkhazia