I don't think it would change much on the international scale. The Communists still have the mainland, and if the geopolitical realities of the time demands, the US and other countries would still switch to Beijing. Not to mention, being closer to the mainland and already infested with communist guerillas, Hainan could potentially slip under communist control in future. That it was overrun at the end of the Civil War has as much to do with collapsing Nationalist morale and incompetence as the communists already in position to clear the beachheads for their admittedly woeful amphibious forces.
As for what happens with a KMT Taiwan, well, Chiang and co have a good population base to draw administrators from to run Taiwan, if already compromised by communist sympathies. Taiwanese-born Han and aborigines could find themselves even more marginalized as Japanese sympathizers, and depending on where the KMT capital will be, could become a virtual colony. The seat will likely be Taipei, as per OTL, but I can see the KMT trying for Haikou or another city in Hainan just to make a point (before shelling from the mainland become too intense). Paradoxically, having Hainan would heighten Taiwanese desires for independence, as Chiang would probably prioritize Hainanese Chinese over Taiwanese, being more Mainlander and 'untainted' by Japanese influence. The KMT might even attempt to colonize Taiwan with Hainan 'loyalists', which would likely raise the locals' ire even further.