There is very little about the Chinese economy today that can truly be called communist. In fact, we could go farther and say that there is nothing that is uniquely communist about their economy.
There are some things about their economy that could be seen as communist. Most importantly, their government has a very large part in running their economy. The government owns many companies that have very large parts of the market in various parts of the economy. The government, to some degree, sets the priorities for the economy instead of allowing market forces to do so.
However, these things are not unique to communism. Japan, for example, was always seen as a capitalist country and yet it had a government that did a lot to determine which industries would be promoted and which would not. Countries like France have semi-nationalized companies in important sectors of the economy. China may go farther, but it is not qualitatively different.
Most importantly, China’s economy does not show any tendency towards trying to ensure equality like communism is supposed to. There is serious discontent on the left in China because the country has gone so far away from Marxist ideals. The growing inequality in China is the most obvious sign that their economy is not truly communist.
There is a reason that the Heritage Foundation/Wall Street Journal Index of Economic Freedom for 2016 ranks the People's Republic of China as having the 144th freest economy out of 178 nations ranked. While capitalism has attained a firm foothold in China since the late Chinese leader Deng Xiaopin introduced his dramatic shift in economic policy following his predecessor, Mao Zedong's death, the Chinese economy can not be considered to be based primarily on free market economics. On the contrary, despite a booming, largely free-market capitalist system at the lower level, the Chinese economy remains tethered to Chinese government dictates. So-called state-owned enterprises, or SOEs, continue to control most major Chinese industries, including banking, energy, transportation, and defense.
The Chinese economy is difficult to pigeonhole. Born of the devastation of years of civil war and the destruction wrought during the Second World War, it has become a hybrid of authoritarian and capitalist models. As noted above, following the doctrine and extremely destructive rule of Chairman Mao, his successor, Deng, recognized the need to modernize and grow the Chinese economy in order to thrust that massive country into the ranks of the technologically-advanced powers of Europe and North America. It did not go unnoticed among Deng and his followers that China, emerging from the Cultural Revolution, lagged well-behind such tiny neighboring countries and city-states as Singapore, Taiwan, and Hong Kong, to say nothing of the economic colossus just across the Sea of Japan. Deng was sufficiently astute to recognize that communist economic theories did not provide the basis for the level of economic growth necessary to support the nation's population and the technological development required to become a major power. And, he was right.
Over the last 40 years, the Chinese economy has steadily grown to become the second-largest in the world, recently supplanting Japan. It did this by opening up its economy to foreign investment (albeit, under very strict terms) and allowing for free market business practices. Consequently, there is a vibrant free market system that has propelled hundreds of millions of Chinese into the ranks of the middle class and the wealthy, In fact, the Chinese middle class numbers over 300 million people, the size of the entire U.S. population, and well-over 2 million millionaires, second only to the United States. That economic growth owes an awful lot to the implementation of free market principles.
Despite its opening to free market economic principles and to foreign investment, China remains, as noted earlier, controlled by its central government, and that central government retains control of the nation's major industries. In contrast to the United States, which has traditionally eschewed government-directed industrial policies, China is the exact opposite. The Communist Party of the PRC zealously clings to its control of the direction of the nation's economy and its control of the country's major industries is its greatest asset in that regard.