The only reason these western supremacists chose China as their rival is the same reason Indians chose China as a rival: It flatters themselves.
They seem themselves as China's equal as a civilisation, in fact the West wishes it was China judging by the recent outburst of 'Snowteps' on Twitter and by how they try to claim all Chinese inventions and advances as their own. For Indians, who were not even a united polity until the British organised the subcontinent around their railways to better pilfer the land, comparing themselves to China raises their stature amongst Anglos who have convinced themselves that the indians who loquaciously flatter them, will willingly fight and die for the white western order.