What was the significance of naming almost every (ancient to early modern) time period in Chinese history as a "dynasty"?
Egyptian royalty is referred to by dynasty, usually numbered as in the 23rd dynasty.
Similar with Roman emperors, except they are given proper names as there were less of them, Julio-Claudian dynasty, Severan dynasty, Flavian dynasty etc.
English monarchs generally don't. You'll mostly see them referred to as House of Wessex rather than The Wessex Dynasty.