the book advocates for “stakeholder capitalism” instead of “stockholder capitalism”

I think the distinction is made to distinguish between different aspects of capitalism, as shareholder capitalism reflects some of the most extreme aspects of capitalism. As for the context of advocacy: “stakeholder capitalism” is the idea that you can make capitalism less bad by tying involvement with ownership: no stock market, no absentee landlordism, no monopoly acquisitions, etc. As something one would advocate, it can range from slightly-left-of-whatever-you-would-describe-Elizabeth-Warren-to-be to Socialism-in-Disguise.

This system, in which state bureaucrats managed large chunks of the economy, ranging from transportation to energy, stayed in place well into the 1970s.

This book refrains from naming it, but Varoufakis calls the system from WWII to 1973 the "Global Plan", and the era that followed the Global Minotaur. In the framing of above, this is when Nixon ended the Bretton Woods system and "shareholder capitalism" completely devoured anything left of managerial regulated Keynesian-influenced Capitalism. Xi's China definite draws from the pre-1973 American capitalist model that worked so well, though while Keynes was perfectly satisfied preserving a functioning version of capitalism for the time being, Xi Jinping describes it as a stepping stone towards socialism: the "initial stage of socialism" according to Xi Jinping Thought (a stage that doesn't seem to have much room for labor rights).