You have to consider the population density in China. One nuke aimed at an 'important target' could pretty easily kill a few million Chinese as collateral.
This would obviously give China all rights to launch a counterattack.
Unfortunately one Chinese nuke cannot do the same to Americans because Americans just don't live densely enough, which means for a sufficient response China probably needs to launch 5+ nukes per one American nuke.
Of course, the Americans will just launch four or five nukes in response, which will kill ~20-30 million more Chinese. At which point, everyone will be nuking each other.
TLDR There is no such thing as limited nuclear war because any limited strike on China will probably kill enough people to justify a massive counterattack, at which point full nuclear war will have begun.
I made a previous writeup on China's current position in a nuclear exchange with the US: https://lemmygrad.ml/post/5407827/4903187