Earlier quoted context omitted.
Not defending Tesla but battery range is really hard without context. Kinetic energy is velocity^2, which means moving twice the speed takes 4X the energy. They probably can get the right estimate for a destination because it knows the speed limit for the route and using that as your velocity can give you a better answer.
"...moving twice the speed takes 4X the energy..." That's not quite right. The power required to maintain a constant velocity v against a constant drag force of F is P = Fv. With air drag on a car moving at highway speeds, the drag force F actually depends on v: it's proportional to the square of v, i.e. F ~ v^2. All together then: P ~ v^3 So doubling the speed will increase the required power by a factor of eight.
If the power is 8x higher and the speed is 2x higher then the energy per mile must be 4x higher, as he says.