:::Whoop-dee-doo, one source, written by a non-native English speaker (Chen Jian).  The author clearly is trying to impose a context greater than what is given with the name Zhongguo because he is using his unique interpretation (translation) of Zhongguo to make a point for his thesis (notice that he has to argue that the Chinese think that "China is superior to any other people" in order to make his point, he can't actually cite anything from the actual historic usage of the term Zhongguo). The character zhong doesn't mean "central" in the literal context of the name Zhongguo.  "Central" is too narrow a translation for the name Zhongguo.  Also, Zhongguo and "All under heaven" (tianxia) are two different concepts.   

 Zhongguo translated literally in other languages (from other Wikipedias): 
 German: Reich der Mitte 
 French: Pays du Milieu 
 Italian: Regno di Mezzo 
 Swedish: Mittens Rike 
 Dutch: Het Rijk van het Midden 
 Danish: Riget i midten 
 Russian: срединное государство (sredīnnoe gosudarstvo)