Although you can play Tropico in various different ways, I don't think there is enough differentiation between running the island in a communist manner, or a capitalist manner. ... However, everything on Tropico is state-owned, because all profits go to you -- so it could always be called state-socialist. ...
Let us remember that this is a game and NOT an instructional simulation. It had to make its own financial way in the open (not free) market as an amusement - in competition with other games of many kinds. A primary question in designing a game is how to keep the buyer\player busy and happy without becoming frustrated.
According to all the suggestions\demands for a non-state owned economic sector, the private activity would be capitalist and run by a background program (part of the game engine). Just a little realistic thought about this would indicate that such a "game" just won't sell without naked women cavorting on the beach to amuse the player while the program runs.
State owned capitalism is not unknown the real world because with a non-democratic government the property and money owners may be also the persons in control of the government. When you start devising an economic simulation (or game), you need to examine carefully the assumptions you make from politically slanted textbooks.
For example, why are democratically run political systems symbiotic with free market economic systems as claimed by the capitalists - especially in the U.S.? In a political democracy, each natural person has one vote. However, in free market economic systems, each natural person and each of a variety of artificial persons all have purchasing or voting power according to a wealth (usually money) system which allocates power in a very complicated way. Logically, these two systems are diametrically at odds with each other. Typically, the undemocratic wealth based economic system overcomes and destroys the democratic political system.
The Golden Rule triumphs -- who has the Gold, rules. Shake off your assumptions and play the game to satisfy either the communist faction or the capitalist faction. That should be sufficient to satisfy your political prejudices about the economic system.