You are a start-up company new to mars sent by the government which are attempting to create long-lasting colonies through private enterprise fulfilling market forces. Your goal is to subvert the governments goal and eliminate all other players. So, who's providing the debt? There is no private enterprise already established, so you cannot take out a loan from them. Look at the clock, each tick is 10 minutes of ingame time. It takes 12.5 minutes on average for a communication to get from mars to earth, another 12.5 minutes to get back. This means you are not getting your debt from anywhere on Earth, indeed it is the colony governments themselves that are footing the bill for you, lending you money that was being lent to them as their own debt. Each government would be registered as an independant country, recieving funding directly from investors or from the governments of Earth. Now think about the interest rates as well, why are they daily? Because the rate of growth of the colony is a daily thing, everyones moving at lightning speed and your debt is paid by the investors of the colonies. Your debt is effectively a part of a countries debt, which is part of why the debt acts wierdly, any debt you take on is listed as the colonies debt overall back on Earth. The system of debt used here is not true debt, it is the governments lending you money, subsidising you in exchange for becoming self-sufficient with your help, and then you pay them back later. The more debt you have, the more debt they have so the harder it is for them to borrow money back on Earth, so the more interest they claim you owe the them and therefore the tax payer later on. This means the system is realistic, because it's a new and different system of lending. When you buy a company, you are not taking on their debt, instead the government just writes it off, they will probably be compensated by Earth for every failed private colony attempt later, since it was their idea, so it doesn't get reflected in your own stock price.
TL;DR: This debt system is neither a country nor a private enterprise system, thus it can be anything mohawk wants it to be, but it does make sense as a possible way a martian colony might handle debt.