To answer whether Genghis Khan is Chinese, we must first consider the question, why do we care so Chinese much about whether Genghis Khan is Chinese?
In fact, Russians, Uzbeks, Turkmenistans, Iraqi Iranians who are in the same situation as us will not dwell on this. At that time, the Mongols occupied the Principality of Churos (the predecessor of present-day Russia), Khwarazm (the predecessor of present-day Turkmenistan, Uzbekistan), and the Arab Abbasid Dynasty (the predecessor of present-day Iran in Iraq). But few people in these countries have wrestled with the question of whether Genghis Khan was a man of their country. In a word, they would not consider Genghis Khan to be the ancestor of their country.
So why don't people in these places wonder if Genghis Khan is their ancestor, but we Chinese have to dwell on this?

(Genghis Khan)
In fact, Chinese dwelling on this point is actually very reasonable. Why?
First, China's history has never been broken.
In the history of world civilization, China is the only country in the ancient civilization of the world that has continued to the present, and history has never been broken. And other ancient civilizations, as well as countries that developed later, their civilizations have been broken.
The main reason why the civilization of these countries will be broken is the invasion of foreign nations. The way the foreign tribes invaded was very barbaric, and these new peoples either drove the indigenous people away or killed them all. In short, it is the foreign peoples who have completely replaced the peoples who originally lived here.
That is to say, although the Mongols once occupied the land of Russians and Iraqis, the Russians and Iraqis at that time were different from the Russians and Iraqis today. Later, after the Mongols occupied these places for a period of time, they were occupied by the peoples who invaded from other places. In this way, these lands are actually inhabited by three kinds of people. Of course, they have integration, but the inheritance relationship is not obvious, so the people who live in these places now will certainly not consider this problem.
Even if the Mongols once occupied China and established the Yuan Dynasty in China, in fact, the indigenous people who lived in these lands in China at that time still lived in this land, they were not extinct, nor did they migrate to other places. Not only that, the Han chinese also intermarried with the Mongols during the Yuan Dynasty, assimilating a large number of Mongols, so that the descendants of the Mongols also became Han Chinese.
It is precisely because the history of China has not been broken, and the Mongols and the Han people of the Central Plains have formed a blood-linked relationship, that we will wonder whether Genghis Khan is Chinese.
(Establish the Yuan Dadu, figure to take its meaning)
Second, in ancient China, there was a perfect system of clans.
In ancient times, there was a clan relationship between the Central Plains countries and the surrounding ethnic minorities. Although the surrounding ethnic minority countries often attack the Central Plains countries, most of the time, the minority countries will recognize the Central Plains countries as the suzerainty, and the Central Plains countries will also recognize the surrounding ethnic minorities as vassal states.
Although this kind of vassal state does not belong entirely to the Central Plains, it is still included in the scope of its own "imperial favor and irradiation" by the Chinese state. Therefore, in this sense, it is also reasonable for the people in these domains to say that they are Chinese.
Although the control ability of the Song Dynasty was already quite weak at that time, the Liao, Western Xia, Jin, and Mongolia no longer formed a clan relationship with the Song Dynasty. But this has been the case in history, and it has existed since. Therefore, from this point of view, it makes sense to say that Genghis Khan is Chinese.
China is now a multi-ethnic unified country.
We can make an analogy that a great river eventually forms and even flows into the sea, which is formed by the convergence of many tributaries. These tributaries, although not named by the great river in the early days, were still part of the great river.
China is now a unified multi-ethnic country. Even if the Mongols and the Han Chinese in the Central Plains have no relationship in history, there has been no intersection. However, because they are now part of China, it makes perfect sense that we call Genghis Khan, the ancestor of the Mongols, Chinese.
This is not obvious in foreign countries, so foreigners do not think about it in this way.
(Mongol cavalry)
Fourth, the spiritual temperament of Genghis Khan and Chinese is the same.
In fact, in our conception, our ancient state was dominant. The Great Han Dynasty, the Great Tang Dynasty, has all played a prestige in the world. The Mongols, led by Genghis Khan, also made a name for themselves in the world. These two spiritual temperaments are the same.
The ancestors of the Mongols have also been influenced by the Central Plains culture many times, and their spiritual temperament is also inherited from the Central Plains civilization. This is a cultural bloodline relationship that cannot be erased
From the above four aspects of analysis, we understand why we care so much about whether Genghis Khan is Chinese.
At the same time, it also answers the question of whether Genghis Khan Chinese.
(References: "History of the Yuan", "Secret History of Mongolia")