If China decides to shoot back, all bets are off. It would be exactly the error the Japanese made when they attacked Pearl Harbor and thought they can get away with it. That would directly affect the West and our leaders could not say anymore "will be fine, we're taking the high road here" unless they want to be lynched by a mob.
Also everyone knows that the US is both highly militaristic and highly jingoistic.
That was certainly true up through the early 2000s, but this stereotype is by now out of date. On the left, America is self-loathing, and on the right it's become quite isolationist.
Terrorist attacks like 9/11 leave doubt about who to go after and at what scale to retaliate but a clear attack on a city by a foreign state as an act of war is a different thing. Gloves would come off and the complete full force of every resource ( military, political, economic, etc ) would be brought to bear.
It depends on the specifics, of course. If a specific country directly attacked the US, of course I'd expect (and even demand) a military response. But these days, I wouldn't expect a non-state's terrorist attack to lead to the sort of misguided, ill-informed adventurism that ultimately led us to invade Iraq.
Also ++ for the use of jingoistic. :)
See also: Korean War, where Chinese intervened to stop the US-allied South from winning against the North.
You remember Kim's brother VXed in Malaysia? He was China's bid on NK throne. China was trying to launch a coup in NK.
China been trying to seize power in NK for decades.
NK-China relations are complicated ones. China wants NK, but is afraid of losing NK if their machinations flop, and push the NK towards the West.
>A thinking that they can win
The only way to talk about war is to be prepared to understand 'the other side' of your argument. In this case, you're setting yourself up to have to answer the question: in the 21st century, which nation state has started the most wars, committed violent hostilities, and murdered innocent citizens at massive scales, the most?
A thinking that they can win: Tojikistan, Karabag, Transnistria, Georgia, Donbas, Crimea, Syria, Libya — all set a very damning precedent of the West conceding to use of force.