Those claims related to changing regimes are of course disingenuous and only aimed at creating a false narrative. It is fake history for political purposes.
Now, there has been (arguably still is) a civil war and the overall territory of China is split with both sides claiming the whole but only one side is strong enough to think they still have a shot a it.
Now, to go back to the article, it serves the US' interests to support one side against the other hence why they do it, in the same way that it serves their interests to 'grab' Ukraine against Russia. It's the same old global Great Game.
Today Qing are as relevant, as Russian historical claims on California.
There's no way the Russian influence in California can be compared with the Han Chinese influence on Taiwan.
Serious lack of consistency.
But then, my understanding is wrong about a lot of things.
A very important detail indeed.