That game has no more basis in reality than the lunatic national strategies devised by the US and CCCP in 1963.
Major escalation is a matter of order of magnitude. When one thinks nuclear war, one must look to historical comparators more applicable than WW II which left at least one international core transportation / industrial hub intact. (Post WW II that would be the western hemisphere.). Since a presumed Russian strategy would be against the western coalition as a block, that means western Europe and the North American continent are hammered. We have never seen that historically. The closest event is the contiguous fall of the Roman Empire and the fall of the Jin Dynasty in China. Both are fifth century common era events followed by mass deaths and economic and political dislocations, but still do not describe the kind of chaos a small nuclear war would have on a global economy. There would be no mass population relocations and no political re-orderings except on the basis of existing survivor power centers, which incidentally would not include China, as that nation was to be targeted conjointly with Russia.
Anyway...
Both of those economic complexes are wiped out, Africa, starves and becomes a hotbed for internecine warfare as water wars break out (as they are about to do now) and the diseases kept barely in check now, are unleashed upon the hapless populations.
The only possible organized remnants who could maintain a reasonable 20th century level tech base post limited exchange would be the South American states. Rational conclusion? Portuguese becomes the new language of commerce and diplomacy. Brazil picks up the pieces.
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Depends on which part of Asia. If one lives near a port, one is dead. If one lives in the deserts, potable water becomes even more precious. Life already marginal for many human nomadic tribes becomes almost impossible. If one lives in Siberia and is not dead, then it is suddenly the 14th century all over again. Hunters will do okay, but everyone else dies. Western Russia? One presumes the same as western Europe. If one is not dead it is suddenly the 14th century for them too with disease rampant, no water, no food and way too many mouths to feed for what food, contaminated or otherwise, is left. Probably a harsh series of winters and hot zones that will last for centuries depending on what was nearby to be irradiated will be added to the situation.
Hobbes is the condition. Humanity will survive. It will take an estimated 500 years to recover.
Only thing is... The ability to scratch out easy resources that this civilization is built upon will be gone. If we go down, that is it for advanced technology as WE understand it. Things will be a lot harder for the post nuclear war survivors. Plastics for example will be extremely difficult for them to replicate. Just getting back to the 19th century with reliable mass produced steel in bulk will be another bolo.
Aluminum? Forget it. Unless someone can figure out a way to replicate our electrical technology without copper. (Irradiated. Strategic resources mines and refineries will of course be targeted; so goodbye oil, too.)