Very clever propaganda at work in this film, both subtle and obvious. You had the blatant Cold War, East vs West symbolism as well as the "We're doing it for the principle, not the money" aspect which automatically grants higher ground for all American military endeavors from then on in the minds of the public but the finer details really make you think:
Apollo was a sun god. Drago represents a dragon which "kills" the sun during an eclipse and thus is also the moon. When he steps in the ring Apollo aka the sun shows he's repping the Bull aka Taurus:
Complete with the song and dance (linked with the sun god Apollo) and material excess (Taurian traits) whilst the bear is much larger, more menacing, austere and standing there quietly. The Russian people claim descent from the Mother Bear which is why the image is linked with the country and you'll notice how Dragos wife is shown as having more clout than him repeatedly as well as speaking for him. The constellation Draco is right next to The Great Bear in the night sky.
Financial markets - Bull and Bear. The Cold War was fought primarily on economic grounds. Also consider that Russia and China are both Communist countries and the dragon links should become even more obvious.
Now the question is
why was all of this symbolism woven into the movie? What did it do to your awareness as you witnessed it? Why do most people lack the insight to put together the pieces and meaning of what they're seeing but accept it anyway?
Really this is just a tiny bit of what was on display as some aspects used are really, really obtuse but it should be enough to make you think.