It is not really that ASB, as the oil can still form but just not be trapped in the proper rock structure or end up becoming another hydrocarbon product like natural gas or coal. The vast majority of hydrocarbons ever present on Earth failed to be trapped by the right rock structure and out of the remainder most went on to become natural gas or coal.
You could really look at several options with this. The Middle East could end up having vast natural gas fields, in which case they become wealthy nations starting in the 1970s and natural gas becomes a big export globally. You could also have a coal rich Middle East, which would most likely end up like the resource rich nations of Africa that remain undeveloped due to lack of infrastructure and a trained labor force (coal is much harder to transport than oil and gas, especially through desert plains without rivers that other regions use to move bulk goods). Another option is that the Middle East gets nothing at all, in which case it would probably remain sparsely populated and nomadic outside of select areas like the Tigris and Euphrates River valley and pearl and fishing villages in Qatar and the UAE (if the UAE ever forms without oil).