Well funnily enough even though they're greek they're still quite popular with a lot of people from the middle-east.
And I LOVE THEM! Why you ask? Oh I don't know, my mother was engaged(and we lived with) a man who was from Lebanon for 6 years. After that long one becomes a huge fan of all the food their family ate.
We used to have this great place in my old city called "Harazdan Chicken" which had great food especially GYROS! *drools a lil*
And if I'm not mistaken the sauce you're all referring to is 'tzatziki' sauce.