This looks like it would run a little 3-phase motor at variable speed, continually. Such motors are used in hard disks to turn the platters, it is basically a small AC motor meant to run continually, and not really a stepper motor. Like other AC motors, it may likely have a lower frequency limit below which it will not be able to start or remain turning, and when stopped, there is little or no holding torque.
The commonly seen stepper motors that are used for finely positioning things, have 2 or 4 coils that are driven with quadrature signals (90 degrees out of phase). However, hooking three of the 4 coils in such a stepper-motor might make it run, though somewhat unhappily here...
Also, there is the matter of the transistor threshold voltages that Audioguru mentions. Using a CMOS 4584 at 12V instead of the 74AC14 might work better. with the transistors shown.
Ashtead