No, they are not.
The PRC leadership inhereted a sixty year struggle with Taiwan. Since their grasp on power is waning, they cannot afford to be openly embarassed by Taiwan. So, when Taiwan acts in a manner that could destabilize the PRC, it puts in jeopardy everything the U.S. is trying to accomplish, in North Korea, in China, and in the region.
Taiwan is rich, free and not ruled by Communists, so they win. The PRC is blocked from taking over 'their own land' by the U.S., which is a continuing source of embarassment for their government, so they lose.
What that has to do with Bin Laden and 9/11 is beyond me.