So your argument is that a right isn't inalienable, but is perfectly squashable, so long as it isn't the government doing it. That sounds like anarcho-capitalism
Not quite. Roman_mir's fantasy world is all about the extreme concentration of power. You don't have to combine terms to make a hybrid description of this idea, as a term already exists for it - fascism. Some people have the mistaken belief that a strong centralized government is required for a fascist state to exist, that is not true. Fascism is just about giving as much of the power as possible to as few of the people as possible, and making sure that the power structure remains that way. This is exactly what roman_mir (aka udachny) wants.
which I always end up confusing with libertarianism.
That is exactly what he wants, is for people to believe that his fascist dream state somehow equates to "liberty".
Nearly any post-apocalyptic dystopia is a libertarian utopia. Non-governmental warlords kiling for power and profit is perfectly fine, so long as they weren't elected.
That pretty well sums it up. Money == power. Buy more, sell less. If you can't afford any, that is your own damned stupid fault, you can go off and die somewhere (at work, if you're lucky).
next you'll tell me murder should be legal because the right to life guarantees the freedom from the death penalty, and not the freedom from being killed by private citizens
Basically, yes. Furthermore as power concentration continues to its extreme, human ownership will be re-instituted. Companies will own people and have the ability to force them to do whatever they want. Sure, we might not see the US government invade Iran under a president Paul, but Coca-Cola, Exxon, and United Defense would be free to force their employees to form an invading army for that function.