Plenty of games, especially strategy and simulator games, have game mechanics related to politics or economics. From Recettear’s “Capitalism Ho!” to Hearts of Iron 4’s focus trees, political descriptions can be added to flavor game mechanics, and because different game devs have endless variation in personal worldviews, these additions can be absurdly bad at times. Even if the mechanic itself is good, it can have dunk-worthy labelling. Post the worst that you can think of, even if they come from an otherwise great game.
I’ll start: In Civilization VI, different government types you choose have different slots for policy cards, which let you select political policy bonuses for your civilization. In the modern age, two of the government types you can choose are “Democracy” and “Communism”. Already this is liberal drivel conflating Communism with non-democracy and “authoritarianism”. But the policy slots for these governments are even dumber, as Democracy gets more “diplomatic” and “economic” policies, and Communism gets more “millitary” policies. Famously, America and the west (clearly what Democracy is inspired by) never destabilized the world with arms manufactoring and invasions, I guess.
There's not really a good way to do it. If your aliens are humanlike in a vague sense, pre-communist and communist, I guess, with pre-communist being synonymous with a home planet centric economy.
You mention different biochemistries, but the issue there is that would require a lot of novel research. Like, what sort of fossil fuels could be produced by such biology? How would this affect technological development? How does class society proceed? Liberal developers aside, it's no wonder games with aliens take place after all this annoying worldbuilding would have relevance. Creating real aliens is a massive undertaking.