Even IF we assume Walmart is a country (which is frankly, absurd), it's still not an example of a free market economy functioning on a scale of (actual) countries. Walmart has retail outlets in numerous countries across the world, and is beholden to the laws/regulations of each of them. It is competing against other companies that are also beholden to these laws. There are far too many forces acting upon it for it to be seen as a 'free market capitalist country' in any respect. Your example is completely and fundamentally unworkable to prove that free market capitalism is enough to run a country.
Don't get me wrong, I want it to be enough. I love capitalism. The proof is in the pudding though, and we've got no pudding. I question if such a country would even be possible in the long term, anyway.
Say we largely remove the government. The governments only role becomes to make and enforce baseline laws about property/human rights, otherwise its a free for all. There would be multiple large companies interested in the game of making and running towns/cities etc. If you wanted to live there, you would need to pay them to maintain the place, all fine because it'd be a consensual agreement between you and them. These towns would likely have their own police forces, and many of them would likely band together under one large board, making the police active pretty much anywhere. It'd get to a point where you need to pay them to live anywhere at all that isn't the middle of nowhere. If you don't pay, the police will come. Anyway long story short the whole thing develops until we're exactly where we started. I believe this is likely the natural order of things.