There is Luxembourgish, which is basically the local dialect codified as one of the official languages of Luxembourg. It's otherwise perfectly understandable for people from adjacent parts of Belgium and Germany. But I guess the locals would see that it really is almost the same.
Similarly to Chinese, Germans see themselves as mostly the same culture. Standarddeutsch is pretty much a fusion between the different varieties and has evolved along with them for a long time; differently from 普通話, which is much younger and the standardized form of a northern variety of Chinese. Germans also really cling to their dialects, and Switzerland and Austria both use slightly different versions of Standarddeutsch.
The opposite example are the varieties of Serbian, Croatian, Bosnian, and Montenegrin, which are quite inter-intelligible, but which are considered as different languages by their speakers.
