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?

had no idea, so asked LLaMa:

There isn't a specific name for the type of government you described [...]
 
The approach you mentioned, where the government runs one competitor in every important industry, is sometimes referred to as a "public enterprise" or "state-owned enterprise" model.