It's not American thinking; these are recognized around the world as universal, inalienable rights. Also universal is every dictator's attempt to portray them as just another opinion which doesn't apply to the "culture" (a usefully indefinable, subjective word) of their country. It's a very old argument, with a disreputable, self-serving cast of advocates.
Following that reasoning, communism, capitalism and international trade are emphatically not part of Chinese culture - not to mention the way people in China now dress and most of the technology and consumer goods they use. Imperial monarchies interspersed with periods of civil war, economic and cultural isolation, and all of it based around Confucianism - that's been the culture since around 250 BCE, and they forcefully rejected Western trade and technology when they encountered it in the mid-19th century (leading to some horrible actions by the UK and other nations).
Chinese people in Taiwan and Hong Kong believe in and live these universal values, and they are the most prosperous, free, and stable regions of China. The values of freedom and democracy apply to other cultures worldwide, from Europe to India to China (Taiwan and Hong Kong) to Japan to South Korea to South Africa to Brazil. It's very hard to argue that they are just one nation's idiosyncrasy.
And who is to say that the people of mainland China don't want these things? Why not ask them? If Xi is so sure that a communist dictatorship has broad support, why not hold a vote?