The author makes some excellent points with regards to the declining value of Thucydides in the nuclear era, particularly in regions such as China where the Kissinger doctrine is in full effect.
A war with China would be economically and physically devastating to both sides, and there is nothing of adequate value in the region to risk that over. Both China and the United States maintain dominant positions that are not threatened by one another.
With these barriers in place, I feel as though America could not easily be pulled into a war with China. China would prefer to abandon North Korea to a war with us, and we would likely prefer to abandon Taiwan rather than war with them.
A problem may arise, however, if either side pressed these factors as a perceived advantage. We might see both sides race to complete objectives in the region, with some minor naval altercations. This could lead to America being 'pushed' into war, as the loss of US servicemen typically demands a response from the American public. Nonetheless, for strictly financial and practical reasons, it seems likely that fighting would be confined to particular theaters surrounding Taiwan, Korea, and the South China Sea. Both sides would prefer a series of controlled skirmishes to an all-out war, even in a hard-push situation.
The result of such skirmishes would remain a net negative, however - the US gains very little from the elimination of North Korea or the permanent independence of Taiwan, to say nothing of the atoll being disputed with Japan. China also gains little from defending North Korea, and taking Taiwan through an extended military campaign would render the island effectively worthless as the valuable production infrastructure there is likely to be destroyed and/or evacuated. By contrast, China can achieve strong regional hegemony through it's current strategy and the United States can maintain strong regional ties by managing the tensions. The current situation is strongly preferable to war for both sides, and so war is tremendously unlikely.