I am not sure that anyone used the term capitalism before Karl Marx wrote Das Kapital. He, of course, drew a line between the capitalists who invested their money in the means of production and thereby claimed profits and the workers who he thought provided all of the value and were entitled to all of the yield of an enterprise.
You are arguing something different and it is getting to be semantics. The problem with the hard work argument is that lots of people work hard who never get rich. Preindustrial Europe and colonial America were societies of artisans and sole proprietors with yoemen farmers, too. They developed a bourgeoise who devised ways of pooling money and sharing risk to embark on bigger ventures, especially trading. They departed from medieval strictures against usury which Islam still preaches. This, strictly speaking, was the birth of capitalism. And, for all intents and purposes there was very little money in those days.
I prefer the term free enterprise to describe my own economic beliefs, because it is free of the Marxist tinge.
I get the Any Rand newsletter, by the way. I doubt she would make the Arabs won the oil lottery argument you began with. So what? Like any other lottery winners the questions are what use are they making of their money and why does the government wrongly take so much of it?
She always referred to her philosophy as "objectivism" and economic system of choice as "Laissez-faire" capitalism, which simply means hands off capitalism.