For Chinese history it never had a medieval ages equivalent to Europe

For China the Confucius and administrative state survived from 223 BC until the Chinese Revolution of 1911

And the Communist takeover in 1949

For China it is very much an example of a frozen civilization

As for Islam it emerged with very few centers of power and a strong administrative state

What made Europeans so successful was the collapse of Central authority and that there were many centres of power

The States in Europe didn't start to centralized power until the 15th century