A most surprising phenomenon! Not only the flight route of ET131 but also the fact that I stumbled across your post as I was tracking for the same flight today (my brother was traveling) and wanted to understand myself what is going on with this flight.
I checked flightaware for the first time and just made couple of clicks on discussion and opened this discussion about the same flight.
The reason for this flight route the way it is shortest route between two points on earth is not a straight line on a flat map, but an arc which is shortest on the globe.
See this link:http://www.gcmap.com/mapui?P=IAD-AUH