I agree with "Withdrawal" but stated "Other" for some of the complexities. As long as they have money, the Saudis and othes will remain players on the world stage. Granted that oil is the source of their income, they nonetheless hold a huge stock of cash in reserve, and little to spend it on. (You don't see them lavishing it on Palestine to make it an Eden.) Once the money run out, so will their friends.
Some historical necessity also comes in to account. Living off Earth, oil is not important at all. The gas giants have all the methane we need, apparently. Some years back, I saw a bumper sticker: EARTH FIRST - we can drill the other planets later.
A book I have on numismatics points out that each shipload of silver and gold looted from the Americas made Spain that much poorer. Wealth is not stuff. We do not need to run out of oil to it to be surpassed for cost-effectivness by several existing alternatives, but especially by something that has not been invented yet.
As to the question, yes, absent oil (or money), the Middle East has not much to commend itself. They are not a manufacturing center. They are not a data center. Or a healthcare center. Or a sports center...