Well, I think the whole point is it doesn't MATTER who launched the nukes first. Both sides are to blame. It would cheapen Fallout's message considerably to say the Chinese or the Americans pushed the button first. No one knows who did it and who responded.
All mention of the outside world suggests that it is destroyed like America. In Point Lookout we learn the UK is a nuclear wasteland, too. China is obviously a nuclear wasteland.
Even third world country's that would not of been hit by nukes would of suffered really badly from climate change etc. Not to mention the total collapse of the global economy. Things for everyone would of gone to hell in a hand basket very quickly.