(its more like having stakes in companies that compose 60% of their GDP, and a lot of that is concentrated in the commanding heights and the rest is often minority stakes through state linked investment firms),
Nope:
The overarching goal was to weave the party “comprehensively” into the fabric of the economy's private sector (Central Organization Department, 2012). Local authorities were directed to establish special agencies to support this goal and firms were requested to seek guidance from local party leaders on important managerial decisions. Further, governments were mandated to use firm-based party cells to advance party-related policy beyond the reach of formal state institutions. The service-oriented character of party organisation was also underlined in a Central Committee document from 2014. While mainly addressing party cells in public organisations, it stipulated that company-based party cells should assist corporate production and operation, and serve as the central mechanism for political leadership of a company's development (政治引领, zhengzhi yinling) (General Office of the Central Committee, 2014).
The 2012 central regulation was personally endorsed by Xi Jinping in several speeches (Xinhua, 2012). The intervention of the top party leadership contributed to a rapid increase in the percentage of private businesses with a party cell embedded in their organisation: from 21 per cent in 2010 to 73 per cent in 2017 (Koss, 2021: 229). Among China's top 500 private companies, 92 per cent had established party cells by 2020 (Chinese Private Enterprise Survey, 2020). Nevertheless, implementation efforts encountered various challenges, including the lack of clear and specific guidelines, instances where business owners co-opted party organisations for their own benefit, and a significant number of inactive party cells (Yan and Huang, 2017).
https://journals.sagepub.com/doi/10.1177/18681026261445459
They literally have to have government official embedded in their corporations