The big Middle-Eastern airlines are mostly not based in oil rich kingdoms. The still-oily parts of the ME are Saudi, Kuwait, Iran, Abu Dhabi, and Oman (with the former 3 being by far predominant). Those are actually the places without the large airlines, except for Etihad in Abu Dhabi (and Etihad is busy failing).
Dubai has very little oil (that is why they run on foreign credit and Vegas-of-the-East marketing image), and Qatar has gas but little oil. Abu Dhabi's oil is not enough to sustain a large economy on its own. Qatar and Abu Dhabi have better things to do with their gas or oil money than permanently subsidise an airline. They are, all of them, trying (cack-handedly but increasingly desperately) to build a non oil-supported economy before the oil (or gas) runs out.
They will not, for they can not, supply more of their dwindling oil money into cheap fuel for their airlines. Their airlines have to stand or fail paying global prices for fuel. Cheap fill-ups forever is a myth.
Now, that doesn't preclude a lot of other support: low interest long term loans, very favourable regulatory environment for airport development, favourable route allocation, keeping the staff servile and subdued, and so on. But not cheap fuel.
The ME2 (Etihad won't thrive) will succeed by being Bling-Ryan-Air - dense aircraft crewed by cheap staff operated by a company squeezing every advantage and support that it can out of airports, simply bigger and nicer-looking than Easyjet/Ryanair/Wizz/Southwest - not by being fuelled for pennies from the Sheikh's own well.