Is there a name for the type of government where the government pursues consumer protection, antitrust, etc policy by directly running one competitor in every important industry, instead of making rules for every participant?

China. They have a government mandate to take a 1% minimum stake in any company if they choose (giving them something like a board seat with a lot of power) and use this as a legal cudgel to control their behavior. I don't think it would work for a government to directly launch competitors but... maybe it can work!!