If I plot a line between Azerbaijan and Grozny, even if I go around the Caucasus over the Caspian, crashing in Kazakhstan seems way, way off.
Also, the time between the 'bird strike' and the crash is 20+ minutes, so they might have been trying to fly towards an airport with a larger runway or better emergency crews. Or maybe just an airport where repair crew were stationed to fix whatever was wrong with the plane.
I think it was more likely that that happened to be the direction the plane was pointing when it got hit by the missile and lost control surfaces, so that is where the pilots went.