Poverty is not eliminated in China, at all. The fact that they lifted a lot of people out of poverty doesn't necessarily mean they can lift all people out of poverty. Nobody else has achieved that. It's not as easy as you make out.

Also: the way they lifted all those people out of poverty was basically by freeing them to lift themselves out of poverty, by adopting an essentially capitalist system. You could say: they simply stopped holding people in poverty.