Why no China?

[Legbreaker]

The Soviets were initially very restrained and only used tactical nukes against military targets in the west. It was Nato who escalated to theater nuclear weapons in September against "an array of industrial targets and port cities in the western Soviet Union".
The Soviets did not escalate, but retaliated.
BOTH sides had ample opportunities to de-escalate, the first earlier in July when the conventional Nato advance could have been halted at the Russian border, BUT I fully understand no commander in their right mind would want to take the pressure off an opponent and give them time to regroup.
The Soviets didn't HAVE to strike against the US, but remember they'd already suffered numerous strikes to their own cities and civilians at that point. To not strike would be to show weakness, and also allow the US to retain full industrial and economic capacity against their own already decimated infrastructure.

Stepping back you can see the chain of events which kicked off in China leading to nuclear war. There were plenty of opportunities to defuse the situation, but plenty of reasons not to do so as well.