Actually, only the Russians that tend to make the news in European and Western hemisphere papers are Caucasian. A lot of Russians are all or partly Asian. It’s just that the capital of Russia is mostly full of Caucasians.
Russian leaders have tried to Westernize (ie “Europeanize”) Russia for several hundred years with varying success, but their efforts have mostly affected the bit that is on the European continent anyway.
Of course, since we don’t hear from them much, it could be that the Asians encompassed by Russia don’t consider themselves Russian, just as those living in all the Soviet Republics were so quick to separate themselves from Russia.