Since market conditions are perpetually changing, successful entrepreneurs are those who can adapt and take advantage of these changes. In some cases that probably will mean that the rich will get richer since their ability to create wealth relies on this trait to begin with. However, in many cases these changing conditions give other folks opportunities to create wealth for themselves through innovation and fresh thinking.
In other words, the way to get rich and stay rich in a market economy is to produce things that other people want. While there are always going to be some folks who have vastly more wealth than the median average, the market at least gives everyone the opportunity to move up the socioeconomic ladder.
As you point out, it is the political economy that leads to real income inequality. We can find examples in the communist countries. The rulers enjoy a much better standard of living than the ruled. Unfortunately, this is becoming the norm here in the US as well. The Federal Reserve doles out trillions to its minions while the masses are happy with rental assistance and food stamps. Meanwhile, the State imposes regulations that benefit the large, established players while putting the little guy out of business (if he can even start).
If we look at something like intellectual property (IP), it becomes even more apparent that it is the State and not the market that produces economic inequality. For instance, U2’s Bono is known for his philanthropy. However, in the New York Times he wrote an Op-ed supporting State protection of IP. So let’s say that you want to start a radio station somewhere in Africa. According to Bono, unless you have his permission to play his music, you can’t put it on your station, even if you have acquired it in physical or digital form. Way to go, Bono! Thanks to you, the ability of our hypothetical African entrepreneurs to better their lives through economic progress is greatly hampered. Bono says that IP protects fledgling artists. That is bunk! Fledgling artists often release their stuff for free hoping to build a following (as the Mises Institute does with its material). IP protects the established artists and the big production/distribution companies, i.e the rich. (Granted, my Bono example is more complex in real life as we are dealing with contract law, etc. Even some libertarians would disagree with me. See Murray Rothbard or Stephan Kinsella on the Mises website for good discussions on IP and copyright versus patent.)
Patents are another good example. Let’s say you want to start a service that builds cheap replacement parts for appliances. Not only would you benefit, but so would the consumer. Well, you can’t. At least not without getting permission from the appliance makers to do so. What if you have a great idea that would improve some existing technology? Again, you usually have to gain permission from the patent holder.
As we can see, IP does not protect creativity, but it does hamper the ability of new entrepreneurs to improve on existing technology. On the other hand, things like open source software give provide real world examples of how a truly free market would work.