Unfortunately Piekoff can't seem to make a coherent point here. He doesn't explain how the "West" came to own the oil in Arab countries. He rails against collectivism but had the audacity to talk about the "West's" ownership in oil.
Then he jumps from talking about the bad Arab dictators to talking about the Ayatollah in Iran some undisclosed number of years after the oil rights were ceded.
He's not doing a very good job. He's necessarily having to ignore whole portions of history that doesn't suit his purpose. Lies of omission.
The question of claiming unclaimed property is very difficult, and it is central to any theory of property rights. I am fully aware of the need to systematize it, and in fact was preparing a theoretical article on this, that after 9/11 needed major reworking. We'll return to that if you keep yourself from getting banned :)))
Here is a short outline. Oil under someone else's desert is unclaimed property. The property right to oil go to the one with technology to extract it. The only way to argue otherwise is to say that the government claims the property just by the virtue of a national border, a dubious proposition.