Why is the Russian mafia so influential?

 The "Russian Mafia" you're picturing is a collection of groups with roots in the Soviet penal system. For approximately 20 years, they took advantage of the disarray brought on by the collapse of the USSR to terrorise both the former Eastern Bloc and the Russian diaspora, frequently working in tandem with rising Russian billionaires and former Soviet security personnel.

Brooklyn, New York, gangster Boris Nayfeld is Russian.

Because they had nothing to lose and didn't give a f*** when they first exploded onto the American and European criminal underworlds, they were (past tense) feared. They tended to play by different norms that more experienced mafia had established and were more aggressive, careless, and violent.

The "new" ethnic gangs that emerge in any new diaspora that is escaping a catastrophe are typically hungry and desperate. Depending on where you resided in the 1980s, Colombians and ultra-violent Vietnamese gangs exerted pressure on American gangs. Russians were involved in the 1990s. Albanians replaced the Russians as the ferocious outlaws. In the future, former NK SOF turned North Korean mob members will terrorise the Pacific Rim's criminal underworld. We keep going round and round.