You are right that so-called modernity, as you put it, no longer belongs just to the West. We have managed to fashion it to fit the values of an Islamic society just as the Chinese have been able to style economic prosperity, science, technology to their ancient civilizational ways.
From a more philosophical point of view, though, I would say that the concept of modernity is itself debatable. More properly, we should talk about fundamental values – social justice, equality, respect for the faiths, languages and ways of others; a governing system and economy that delivers the goods to its people.
When you approach the issue in this way, and explain to the people that their values are not in contradiction with new ways and means to improve their lives, they take ownership of the process of development. Greater prosperity flows from their confidence and willingness to open up and engage the world on their own terms. Because of this sense of ownership, the idea of democracy becomes more strongly rooted. It can’t be easily dislodged because the people and their government are aligned in their aspirations.
This is the reform path we are taking in Turkey today. I think you will see China and, despite its present challenges and difficulties, also Russia move toward democracy as we understand it: good governance that abides by the rule of law and accountability.
If the idea of “being modern” is imposed from the top by authoritarian means, it doesn’t work. That amounts to social engineering. There is resistance to it because it is seen as importing Western values. We have seen this reaction clearly in the Arab Spring uprisings which overthrew authoritarian “modernizers” across the region. The Arabs are now seeking their own path commensurate with their values.