The strategic nuclear weapons only apply in extreme situations:
The great bulk of international relations happen without conflict, and they strongly depend on the perceived military power of nations. The United States' overwhelming conventional military power has been a guarantor of peace in the western Pacific for decades. If countries there no longer believe the U.S. can or will protect them, then they may arm themselves, which tends to lead to conflict, or they may side with China.
Regarding U.S.-China conflict, unless survival of either country is at stake then there's reason to believe (and hope) that conflicts won't escalate to strategic nuclear weapons and destroying the world. For example, if mainland China attacks Taiwan, would either side use nuclear weapons? If not, then conventional forces come into play.
I don't mean to downplay the risk. Conflicts escalate very easily and unpredictably; that's why the professionals in diplomacy and military affairs are very careful to avoid it, and are careful to choose options that don't escalate it. It's always the amateurs who want to escalate with an angry response, and as a result get masses of people killed and incur extreme costs - because they were angry.