Bill Hayton is correct that Taiwan was not particularly important to Beijing after 1895, because the island was viewed as having been irretrievably lost to Japan. But that history arguably became irrelevant when it was wholly eclipsed in 1949: Chiang Kai-shek made the island strategically important to "China," and Harry Truman endorsed that importance when he came to Chiang's defense in June 1950 (even though Washington had previously been highly ambivalent about Chiang). So one might say that it was the United States that made Taiwan geostrategically important to Beijing--by intervening in the Chinese Civil War in a way that made the island a platform for foreign-backed opposition to the CCP's legitimacy and control.