The story is bulls**t. The story says that the smallest baby weighed 2.5 kg. (5.5 pounds) and there were ten babies. This means that there was well over 25 kg (55 pounds) of weight in just babies. Now add in the over weight that a woman gains during pregnancy which is at least 2 pounds for every pound of baby and that means the woman put on at least 165 pounds during her pregnancy. Obviously the story is fake.
Russian "news outlets" are full of unusual stories. UFO sightings are so popular in the Russian media that there must be a community of extraterrestrials living in Russia and often travelling home to visit family and friends. Big foot/Yeti stories are also popular, obviously a large community of them living in the forests of Russia. Of course there are stories about "regular" humans. Multiple births, two headed or three headed humans etc. All must be more unusual than the news stories from the rest of the world because after all these stories happen in Russia so they must be better and/or more unusual.
Ten babies in a single pregnancy and all survive would have made the news around the world. The link is about 8 babies in a single pregnancy and all survived at Kaiser Permanente Bellflower Medical Center in southern California.
http://www.nytimes.com/2009/01/28/health/28octuplets.html