On the specific issue of HK, it's been part of China for a very long time and only taken away recently. Of course we are not talking about taking back European territories that used to belong to some dynasties briefly. Just those stable ones since Ming and Qing dynasty. As another comment pointed out, although China has been divided many times, the geographic boundaries did not change much, unlike Europe.
Taiwan is more debatable because it was separated from China geographically, culturally and economically for very long periods of time.
It is actually much complicated than those maps showing only one governing body. Actually those maps show precisely the periods of unity (Han, Tang, Yuan, Ming, Qing) where only one major power governs, as well as the periods of divisions where foreign ethnicity capture a sizable portion of China.
In latter case, the map fails to capture the lost boundary, like in this case: https://en.wikipedia.org/wiki/Jin_dynasty_(1115%E2%80%931234... where Jin dynasty is in control of majority of the territory and the map only shows the defeated Northern and Southern Sung dynasty. Actually the website that you quoted from also has the information:
> brutal invaders drove the Chinese from their northern territory, forcing them to migrate south and establish a new capital city.
Taiwan is more debatable because it was separated from China geographically, culturally and economically for very long periods of time.