Why is "China" considered one continous empire until the early 20th century

It's not, and certainly not by those who actually study China. You're simply using historian's references for Persia but layman's for China.

This is just a matter of perspective.

What's happening is that people who don't really know East Asian history and linguistics are presenting superficial views on China and that's being compared to what historians have said about Persia. If you come here, you're going to see the exact opposite. We talk about the Ming and Western Xia and Goryo and the Wa, but the average person on the street won't know about the Parthians.

Where is this question coming from? Who is considering that China is a continuous empire?

It is really just an issue of semantics. Replace the word "Empire" in any Persian polity with the word "Dynasty", and you will get a sense of what I mean. What in Persia would have been considered a new Empire was called a new Dynasty in China. The Chinese word for Empire is di guo (帝国), but it can be used somewhat interchangeably with chao dai (朝代), the word for Dynasty.

I think you are reading this through something of a Eurocentric lens. After the early Chinese empires of Qin and Han broke down, there followed the "Three Kingdoms" period, in which chinese culture and language developed along very different lines in the North, West, and South. The next dynasty to reunify most of the lands held by the Han Dynasty was the Sui, quickly followed by the Tang. The royal families of these two Dynasties were not wholly ethnically Chinese, and introduced further changes into Chinese society, language, and culture.

Tang fell in 907, and was followed by the "Five Dynasties and Ten Kingdoms" period. The Song Dynasty reunited most of what had made up the Han Empire before themselves going into an agonizing death spiral caused by encroachments from nomadic peoples such as the Tangguts, Khitans, Jurchen, and finally the Mongols.

The Mongols have a brief dynasty called the Yuan, which was overthrown by the native Ming, which was in turn overthrown by the Manchu ethnicity Qing. The Qing lasted right up until 1911, when they were displaced by the Xinhai Revolution, and China descended into the Warlords Era until the CCP reunited most of the former Qing lands in 1949 and declared the People's Republic of China.

The point is, just like in Iran, Empires in China came and went, and they had different ethnic groups in the elite classes as well as different cultural values and languages. We just call them Dynasties in China rather than Empires.

Maybe you mean "why is China considered one continuous civilization"? If so, there have been a few threads on that topic here; here's one from last week ~

Is it fair to say that "Chinese civilization" is more "continuous" than "Western civilization"?