But actually using those nukes on China is not a possibility. The trade relationship between the US and China is simply too valuable. Nuking China would mean was less gold from trade routes and no excess resource trades for gold, forcing the US to dial back the culture and espionage sliders (already obviously running the science slider at 0%--how long is it taking us to research fusion again?). That means unhappiness and vulnerability to annoying Arab and Persian spies.
It's completely unthinkable in the first place. I doubt geopolitics would be particularly relevant in the aftermath of a full-scale US nuclear first strike on China. Maybe it wouldn't be enough to destroy global civilization.
Well, as I already threw out there, I DON'T think it would spell the end of civilization. Any leader who faces such a reality would realize that America is not to be trifled with. IE have nukes or be destroyed, as America is apparently totally fine with annihilating countries (in this scenario). So if you don't have nukes, you probably don't consider a DoW. If you DO have nukes, you realize that America has more nukes than you could possibly stop, so what does your country gain in that scenario? I think the world would vilify America, and be scared of it, but so scared of their own destruction that America would "get away with it" long term. But I imagine all countries WOULD stop trading with the US, and the US would find itself in the toilet economically.
To refer to CIV: Lots of "you nuked our friends" penalties, followed by requests to "stop trading with our worst enemy" which would be accepted, since the ask-ee in said requests also has America as its worst enemy.