It's not that the Communist Party ties itself to unifying China. It's the culture. It's because that the only way to claiming yourself a legitimate Chinese government is to become the conquerer of all China. All dynasties who did not have reign over every parts of China, like Jin and Song, are considered shames in history by the Chinese people.

There is nothing to do with the Communist ideology or any particular party or people. If it were KMT on the mainland and Communist Party on Taiwan, they would do the same.