I know what you mean, but Taipei is the capital of the Republic of China.
Most people are referring to PRC (AKA mainland China, nominally communist) not ROC (AKA Taiwan, a republic) when they say China (at least in the west), so your statement is true but not particularly helpful in this context.
That would be a fun conflation by a Chinese advocate.
Taiwan is Chinese, but they're not communist Chinese. They are the Republic of China, not the People's Republic of China.
Most Taiwanese do not see themselves as Chinese.
> Republic of China
Most Taiwanese would love to change that name, but China is threating war if they do.