Ah but Taiwan is a special municipality and has it’s own government. So this is expected actually. China is actually in a weird situation where there is a rebel government that controls a portion of the country, and they claim their capital is Nanjing. But because the regular government controls Nanjing they have a temporarily administrative centre in Taipei, since it’s the only large city under rebel control. So Taipei is just a capital in China, specifically the capital of Taiwan municipality, but isn’t the capital of China. China actually has many capitals. Hohhot, Lhasa, Nanning, Ürümqi, Taipei, Yinchuan and Beijing. (According to the rebels, it’s only Nanjing).

This is kinda besides the point of whether Taipei is a place or not though. You’re right, it didn’t say it’s in China. You need to click on the article for Taiwan or read further down for that. That’s why I mentioned that it has multiple place-names, so you could look those up on a map. They really should’ve mentioned where the city is, I think that’s pretty standard for an encyclopedia article on a city.