I thought that it had long been believed that the north African jungle cat was the ancestor of our domestic cat as the kittens can be domesticated (unlike the European Wildcat) and when it cross-breeds with the modern domestic cat, the kittens are fertile. It also lives in the area of Egypt, where it is believed that cats were first domesticated by farmers. The Ancient Egyptian economy depended on it's harvest and the grain stores, which cats protected against rats.
So I'm surprised that the DNA suggests the middle east. Wonder where they mean, exactly?