Chinese Taipei vs. China in the Olympic Games

The New York Times has an interesting article about the competition between the Olympic teams from mainland China and from Taiwan, which is officially called Zhongguo Taipei, which roughly translated means Chinese Taipei. Taiwan's status the Olympic Games is as a full member but it is interesting that Taiwan does not get to use its appropriate name during the Games. While yours truly defines Taiwan as a country, China definitely does not see the island in that regard.