Soviet Russia had nothing whatsoever to do with Social Darwinism, ideologically speaking.
Even Stalin's purges or engineered famines weren't tied to Social Darwinism, but were merely the result of a power-crazed, murderous tyrant trying to decimate and terrify his own populace.
As a matter of fact, the ideology behind free market capitalism and the GOP has MUCH more to do with those ideas than anything the Soviets ever did.
For that matter,
Social Darwinism has very little to do with either Darwin or with evolution, despite the name.
As a matter of fact, Darwin felt that "social instincts" such as "sympathy" and "moral sentiments" also evolved through natural selection, and that these resulted in the strengthening of societies in which they occurred, so much so that he wrote about it in Descent of Man:
"The following proposition seems to me in a high degree probable- namely, that any animal whatever, endowed with well-marked social instincts, the parental and filial affections being here included, would inevitably acquire a moral sense or conscience, as soon as its intellectual powers had become as well, or nearly as well developed, as in man. For, firstly, the social instincts lead an animal to take pleasure in the society of its fellows, to feel a certain amount of sympathy with them, and to perform various services for them."
The "fitness" in "survival of the fittest" can take many forms: it can refer to lonely killer species like sharks, it can refer to selfless, self-sacrificial species like ants or bees, and it can refer to species like our own, vacillating somewhere between the two extremes.