GDP is not perfect as among other things it ignores the damage being done to the environment and excludes a lot of things like, for instance, a mother dedicating hours of her time to the teaching of child and, conceptually, it can even be negative - that island of yours being bulldozed by a cyclone and forced to import everything that needs.
However, GDP does not intend to measure power, but output per person. or country.]
"Emerging economy enterprises nowadays relentlessly scale the value chain in a quest to compete on the world stage in part by copying the products of others.
They develop products and services that are dramatically less expensive than their Western equivalents." and they do this by legal and illegal means while placing all sort of barriers to foreign competition.
The problem between China and the USA is that China seems to have already passed that phase in the same way that Japan did it during the 70's.
Economic development is done by stages and the Chinese economy is already at the stage of direct competition with that of the USA creating tensions between the two countries.
Apparently, all systems seem to reach a pick or turning point following by entrance in phase of decline.
