He doesn't. It appears that I wasted my time explaining that oil, or anything else, is not property unless an individual owns it. You had plenty of material on this thread to grasp this notion; if you haven't, it is pointless to re-explain it to you.
I am familiar with the position that natural resources can be claimed by a nation as a whole and that as you say "without government there is no real property ownership". The view that a nation or the government apart from the individuals is a source of property is precisely antithetical to libertarianism. You can argue for the position of course -- you won't be alone doing that, -- but please, don't mislabel it as libertarian.
In historical reality the oil companies were invited by governments to explore oil and were given concessions to that end. So the oil companies typically acted properly even within the imperfect legal framework of the governments. Then at some point the governments demanded that the oil industry be nationalized, -- that is, stolen from the oil companies. Our government, as Peikoff suggests, would be justified in reclaiming that property.
We are talking about land here. Not personal posessions. And no it's not antithetical to libertarianism to understand that the only way you can trade real estate is in the presence of government. The only way one can own land is if there is a piece of paper that says he does. Otherwise he is simply making a claim. One never really owns land.
One can chose a territory and defend it. But one doesn't own land. That is a modern invention. If you owned it, you could take it somewhere else.
Even if your description of libertarian principle were completely true, this statement would be completely false unless you are admitting to U.S. nationalization of the oil companies and believe this is "libertarian."
Because in your scenario, the only individuals having a real claim on that oil are the corporations. The oil companies. End of story. And nobody in the U.S. has a "right" to oil. The only people harmed by the actions of the Arabs were the oil companies. Because Piekoff doesn't like the fact that his gasoline costs a buck and a half a gallon, he thinks that war is the remedy.