Heavens Mandate applies because it is the economic development that Chinas government are enabling which allows them to continue to hold power despite abandoning the Communist ideology that was previously their alleged rationale for holding power.
Dengs 'Socialism with Chinese Characteristics' has largely succeeded for most Chinese people and as long as it continues to most Chinese people are likely to accept the continued rule of the CCP...although if China achieves definitive global dominance Chinese people can be expected to demand more and more 'rights' and 'freedoms' just as the citizens of every empire in history have done.

Now that you mention it, it seems that Heavens Mandate viewed this way would be functioning as a type of unwritten constitution in the way I describe above. I’m just not so sure that it will play out that way without any sort of written, explicit fleshing out of what people should expect guaranteed to them.