China was a center of civilization, it radiated outward in a region that lacked strong institutions and a [written] language, resulting in their evolution being one of syncretism giving the entire region a decidedly Chinese flavor. Where these peripheral regions met other peripheral regions of a center of civilization the culture became more blended, such as in Southeast Asia and Central Asia. If you want one center of civilization to overpower another it requires conquest. Hellenism becoming a veneer for the entire Middle Eastern and Southwest Asian world can be blamed on a mixture of Alexander and colonialism. The Middle Eastern cultural center spread through the Arabic conquests, and thus a conversion of Hellenistic civilization, restored Persian civilization, and Roman civilization was brought via the sword and a period of time. In order to make India and the Middle East into a Chinese flavored region, you need those regions to be conquered by them. This is possible, but it may be more of a European flavor reminiscent of late imperialism, as it is likely that this would be a later development. While Chinese civilization could be exported West and South into these regions, the requirements become increasingly convoluted. Such expansions are usually driven by population pressures, but China tended to collapse under population pressures rather than export itself. It might be possible to make it a more cultural exportation, but we do not really have peaceful conversion to a fundamentally different cultural setting without the sword being involved.