The Russian style goes back to before the Soviets. It’s deep rooted in tradition and the Soviets took it from there: K.V. Gradopolov, then the most important Soviet specialist in Boxing, authored a 1941 work about using proper technique when fist-fighting. In that book, he offered a new exercise, called "group boxing", and he mentioned it was an ancient Russian sport (what he was talking about, was the "Stenka na Stenku" version)