The point is, China's economic development massively accelerated once it massively moved toward the direction of market economies. They still have significant centralization, which is why they will likely reach a ceiling on their productivity, after which growth will be much more tepid, but the point stands.
It seems much more likely that they were benefiting from the catch up factor, as all the low-hanging fruit for raising productivity could be picked in the wake of a large scale roll back of communist restrictions that had been in place for 30 years.
Also, china isn't liberal, that's why it does so well. They also don't have intellectual property.