I'm not an expert, but I do not see how that circuit can provide half stepping.
The motor has four coils (two center-tapped windings). Each winding is driven by the Q and not-Q outputs of a D-type flip flop. Therefore, when one half of a winding is turned on, the other half will always be turned off. So, looking at the entire motor, two coils are always on and two coils are always off.
My understanding of a half stepping sequence for a unipolar motor would require that the driver be able to alternate between one coil on and two coils on. I do not see how this circuit can do that.