Taiwan is more debatable because it was separated from China geographically, culturally and economically for very long periods of time.
I'm not sure I could call this as "not changing much".
http://archive.artsmia.org/art-of-asia/history/ching-dynasty...
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.
http://archive.artsmia.org/art-of-asia/history/dynasty-sung....
>"They just want to take back what used to belong."
How is this different from various historical German ideologies that have centered around "taking back" Greater Germany including the former holdings of the Holy Roman Empire or Prussia? Consider that Otto von Bismarck was still alive when Taiwan was part of Japan.
The desire to fully restore the borders of the Qing is completely understandable and even laudable from the Chinese perspective. The problem is that it's nearly impossible to have a peaceful world if every national or ethnic group feels justified in using the historical borders its ancestors once held as a bar for what they need to "take back", by force if necessary.