The question that needs to be asked is "Is Airmule one of these companies, and are Airmule couriers authorized representatives of Airmule?".

The distinction is not that Airmule is a company that provides services in the manner of a common carrier. It's whether they're recognized as such by the government. This is probably done by filing papers in the US and in China. Then they could answer "We are a common carrier, license number XYZ. Users sign form ABC to become an official Airmail representative."

A slightly less important but still relevant question is whether operating a courier service using an airline which itself offers the same service is a violation of the airline's TOS.