(I'm just an interested amateur who reads a lot so take everything I say below with a grain of salt. I also leave things out for brevity)
Deng Xiaoping (1904–1997) should still get credit for most of what is happening now. China had multiple paths it could have followed when Deng took over, but he was a clever fellow. He made several gradual alternations to rigid socialist and Marxist doctrine and authoritarianism that separated Chinese communism from all others others. He was able to keep hardliners at bay.
1. He declared that: "Socialism means eliminating poverty. Pauperism is not socialism, still less communism." Before Deng all communist countries justified poverty and suffering of the masses as necessary part of struggle towards communist utopia. Deng threw this rationalization away. He essentially adopted the same measure stick to success as capitalism.
2. Deng recognized stuff that worked outside government. 18 households in Xiaogang Village started land reform after a serious drought in secret in 1978 and it started to spread. It was against government rules and even against party doctrine. Instead of prosecuting people Deng endorsed it. Successful land reform has been the starting point for other successful Asian countries as well (see Studwell's "How Asia Works").
3. More meritocracy and checks and balances within the communist party. Before Deng, China was always gravitating towards typical strong man communist dictatorship. There was one dictator on the top and power and orders flowed downwards. Deng adjusted the rules. Government officials were moved to work in different regions from where their personal contacts were (and opportunities to corruption were reduced). Princelings still got into powerful positions but talented newcomers also had a change. There was clear movement towards meritocracy and accountability within the communist party.
After Tiananmen Square protests of 1989 Deng's power started to wane and hardliners gained more power. The momentum of his institutional reforms has carried on but there is constant erosion. The current leader Xi seems to be a typical strongman who tries to get more and more power to himself and his inner circle and this may end all momentum for China that Deng Xiaoping created.