China's goal has been to maintain a nuclear deterrent (make it not worthwhile to strike China) rather than an offensive capability.
if nukes flew then China would likely fragment into many separate countries: its centralized command structure would be destroyed and local politics would be the rule. Look at China's history to see its future after a nuclear war:
It's hard to tell what you intend by your DDG link, but perhaps you are suggesting that, in the case of nuclear war, China will effectively revert to the Warring States Period of 2500 years ago. Is that really your intention? What would the US look like if it were returned to 2500 years ago, before the rise of the Anasazi and the Mound Builders, before the Olmec invented writing? A much more likely outcome than this sort of quasi time travel is that either a post-nuclear US or a post-nuclear China would look like nothing ever seen before in human history, more closely resembling the world in the immediate aftermath of the Chicxulub impact.
Strong central government collapses -> country fractures into regions controlled by warlords -> new strong central government arises. China has seen that movie many, many times in its history.
Similarly, when the strong central government in Mycenaean Greece collapsed in the Bronze Age Collapse, Greece fractured into "regions controlled by warlords." Then one of those warlords, Alexandros, conquered Persia, most of the Mediterranean, Turkey, much what is now Uzbekistan and Turkmenistan, and part of India. Then he died, and his empire fractured into regions controlled by warlords. Then the Roman Republic conquered most of the same region (not coincidentally becoming a Greek-speaking empire in the process), plus part of Britain and most of Western Europe, and fractured into regions controlled by warlords. Then the Holy Roman Empire arose and reunified a lot of those regions, at least in name (arguably, much like the later Zhou) and then fractured into regions controlled by warlords. Then Napoleon arose and reunified a lot of those regions, including parts of Russia that Rome and the Holy Roman Empire had never reached, but that didn't last long, and the warlords retook control from Napoleon pretty quickly. Even the Bourbons got restored! Then Hitler arose and reunified a lot of those regions, but his "country" fractured into regions controlled by warlords even more quickly. Then the European Union arose and reunified a lot of those same regions again by winning the loyalty of local warlords like Charles de Gaulle, Paul-Henri Spaak, and Joseph Luns. Or, alternatively, NATO did. Or the UN.
And you can tell a similar story about Russia.
You could reasonably object that NATO, the EU, the UN, and the Holy Roman Empire aren't or weren't "strong central governments" as we know them today. Well, they weren't Westphalian states, it's true. But neither were any of the reigns of Chinese emperors we're talking about here. And, although if you go to overseas Chinese school you might be taught a simple linear succession of dynasties, the truth in China is much more complicated, just as the truth about western Europe is much more complicated than my linear version above.
What does that have to do with what Russia would do if the nukes started flying? Does the collapse of the Kievan Rus' in the face of the Golden Horde mean that Russia's command structure would collapse in the 20 minutes needed to launch a counterattack? The Scythian king Ateas, from what is now Russia, fought in his dotage and fell in battle with Philip of Macedon in 00339 BCE, and his empire collapsed. Should we thus infer that his successor Vladimir Putin will remain in power too long and make Russia weak, easy pickings for a new conqueror?
Such inferences are obviously ridiculous.