“The Department of State fully recognizes that it may be necessary at some stage for the United States to take military action if [Taiwan] is to be denied to the communists… Such intervention should be publicly based not on obvious American strategic interests but on principles which are likely to have support in the international community, mainly the principle of self-determination of the [Taiwanese] people” — “Memorandum by the Acting Secretary of State to President Truman”

China claims democratically governed Taiwan as its own territory, which the island strongly rejects.

The UN and even the United States also formally recognize Taiwan as a part of the PRC.* There are only a few small countries that recognize Taiwan as a separate entity, and not just a separate entity—there is no "Taiwan" when it comes to governance, but the "Republic of China" with claims to roughly the same territory as the PRC (Reuters acts especially egregiously when they talk about "Taiwan's navy chief" rather than the chief of the ROC Navy), and so you cannot recognize the governance of Taiwan and the PRC but must accept one over the other, and the PRC has proven its legitimacy at every turn. That's why this is never mentioned. The West wants a story of China encroaching on an innocent foreign country and the valiant defense of this country by the West.

*They admit this later and allude to the PRC/ROC conflict, and yet write:

Washington[...] is bound by law to provide Taiwan with the means to defend itself and is the island's most important international backer

Bound by what law? The Taiwan Relations Act passed by US Congress? The article should read: Washington is bound by their own law to provide Taiwan..." It's like how US leaders constantly talk about the obligation of American leadership in the world as if it wasn't them that created this "obligation." Genuine nonsense. For contradictions:

First there's their word (although it's been established that the word of the US means nothing): "The United States acknowledges that all Chinese on either side of the Taiwan Strait maintain there is but one China and that Taiwan is a part of China. The United States Government does not challenge that position. It reaffirms its interest in a peaceful settlement of the Taiwan question by the Chinese themselves. With this prospect in mind, it affirms the ultimate objective of the withdrawal of all U.S. forces and military installations from Taiwan."

And second, their signing of the Cairo Declaration (and Potsdam Proclamation which reaffirms this) in which the U.S. and U.K. (and the Soviet Union) recognized that Japan had “stolen from the Chinese" areas including Taiwan, and agreed to ensure that it was liberated and returned to its former status within China—this is also, some would argue, their word and not legally binding, although the US would still have gone back on their word (in this case with the flourish of a signature).

Taipei says the Chinese territorial claims are void as the People's Republic of China has never governed the island.

This is just tautological drivel.