What is generally agreed upon is that Southern China, and most of South-East Asia was actually Dravidian. This is why we can see the mixed populations of South-East Asia whom can also be dark skined. The "Yellow" people or Mongoloid originated from Mongolia, migrated to the South and mixed with the indigenous peoples.

There is not really enough info to prove that the Shia-Shang Dynasty of China is Dravidian, because it appears that they were absorbed by the much larger Mongoloid population. It would make more sense that the rulers of the Dynasty were Mongoloid while there was a significant mixed or Dravidian population.