I'm not a political scientist so I might just be misunderstanding what you mean by patrimonial, but I don't think that's an appropriate descriptor of "so many" of the oil exporting states. Nor does it seem obvious to me that these states became this way following or as a result of the discovery of oil. There are certainly historical lessons that can be learned about how states have dealt with the discovery of large oil or other forms of natural resource wealth but I don't think the form of government is one of them, particularly given the history of how these forms of government came to power.

For instance, if I'm understanding "patrimonialism" correctly it seems to me that Libya might be the closest to matching that descriptor, and yet Qaddafi's rise to power was more intimately connected with the pan-Arab "Free Officers" movements that came out of Egypt than it was with the discovery of oil.

Iran is another interesting point, in that the Shah ran what was, likewise as far as I understand it, a "patrimonial" state only to be overthrown in a revolution that espoused the doctine of vilayet-e-faqih, the rule of the Islamic jurists, a radically different form of government and rule.