The rooster phenomenon is not limited to any culture or nationality. You can find jerks anywhere, and you will. I think the trick is to LAUGH at them; don't lecture, don't give disapproving looks that they can set themselves against, just LAUGH. Let them know what silly little peasants they are.

As for the "this is my country" bit, just imagine going to YOUR country and trying to explain to the cops why you should be allowed to break the law... That's what these people are doing when they park on the sidewalks or drive aggressively. They are breaking the law and it is NOT okay with law-abiding Qataris. It is only okay to the degree that corruption is tolerated.