At the beginning of modern gymnastics there were two schools of thought. The German was more individual, and performed on apparatus, the Swedish was synchronized team calisthenics, sometimes with clubs and such. Sometimes you can see it in old ceremonies.
There used to be team calisthenics competitions under the Olympic gymnastics header. Then Olympic gymnastics became more standardized, and the Swedish way kind of broke off and got popular for graceful movements and a lack of broken necks. It picked up some pretty props, and became an Olympic sport in its own right. I have utterly no explanation for the leotards.
I'm not really sure what the definition of a sport is, but I think what they do with the apparatus is amazing, and to dance at the same time without looking like they are doing anything technical as far as things like catching the apparatus also amazes me.
I have no idea who should have won, but I don't think Russia should go around saying they were cheated. I've never seen anybody so devastated to have gotten silver in all of Olympic competition as Dina.