Except that that's the conventional journalistic way to refer to leaders who come from the political party with the formal name Communist Party of China (中国共产党). The party has been ruling China as a one-party state, in effect, since 1949, and Marxist-Leninist official ideology (which declares that China is currently in the stage of "socialism," in Marx's view of history) is still the framework for discussing national policy in the state-controlled press.
Unfortunately, the constitution mostly has not been followed.
That's an understatement. Yep, most countries that are ruled by a formal Communist Party have very appealing language in their written constitutions, because the constitutions are strictly propaganda documents, not legal documents that a citizen can take to court to rely on for protection of individual rights.
I'll trust the journalists who are not under direct party control for information about China, thanks.