First of all, the "Middle East" is the location of dozens of independent and soverign countries which presumably each have their own set of principles when at war, so the region as a whole cannot be painted with one brush. Moreover, the concept of "civilized" war is insane. In war, the purpose is to kill as many of your enemies as possible. It is horrible, and some poorly-conceived concepts of "ethical" war don't make one country superior to any other.
It is undeniable that there are actors in the Middle East who do abide by the ethics of war (completely begging the question: what is meant by "ethics of war"?). However, to paint an entire geographic region, and its peoples, with any blanket statement is logically unsupportable. A similar, and absurd, example would be to make a blanket statement like "Does the Middle East eat falafel?" A lot of people in the Middle East eat falafel. The Middle East, per se, doesn't eat anything.
I do not believe the Middle East abides by the ethics of war. To be honest, there's nothing ethical about war. People can opt to be more ethical when involved in wars, but that doesn't make the process ethical. Tensions in the Middle East are too far gone to be concerned with ethics. Considering ethics in that arena is like asking for a death sentence by way of mortar bomb.
We've seen it everywhere from America to the Middle East. No one seems to have a care about the ethics of war anymore and it's a shame. It used to be that certain things wouldn't happen, but now the Middle East cares no longer. They'll gas their own people, kill their own people, and instill tyrants within their own borders.