Communism is by definition stateless, where common ownership of the means of production enables massively more in the way of private enterprise (in the sense of individuals having time to build, make, research, develop projects, offer services, etc) than the fascist state depicted in the game (Fascism itself is often said to lack an economic ideology, frequently finds itself allied with large corporations and I tend to agree that it often plays out as a state-capital alliance in modern times, see Italy and Germany in WW2, or the various fascist/corporate collaborations in the global south), though I agree maybe a better word could be used given how the term kinda carries the connotation of enterprise as in corporate enterprise or a capital venture. I mean it more in the sense of the freedom to do what you want with your own time has been outlawed by the state.
Ideologically you may be mixing up Full Blown Communism with the transitionary state of Socialism, which does tend to carry state monopolies on production as a means of removing the means of production from the hands of the few and democratizing them among the workers directly, typically coordinated into a centralized state. In the world of Rennasistance this period passed for most of the world decades ago, and now everyone is living Fully Automated Luxury Space Communism. I'd say most of the people outside of Neo-Klettgau don't work for anyone but themselves now.