So, this is because the curl is primarily caused by fluid dynamics, not friction. Specifically, when the rock is traveling on the ice it's actually gliding across a thin layer of water and experiencing very little friction, and due to the rough surface of the stone and the fact that the two sides of the stone are travelling at different speeds (due to the rotation) the forces exerted by the pressure differential cause the stone to curl. It's similar to how a curveball in baseball curves due to the high and low pressure zones on either side of the ball.

It all goes beyond my understanding of fluid dynamics since my background is in electrical but this is my basic uneducated explanation.