Welcome.
I tried to get the schematic from that site, but I'm not a member.
I'm thinking there are 2 o/p's from the usb device pwm and direction, and the encoder feeds back the position.
You could convert this to inputs suitable for a stepper motor driver module, which tend to be direction (needs no conversion) and step pulses, the pulses step the motor, so you'd need a system that converted a pwm signal into a pulse frequency, the best way to do that would be to use a micrcontroller, that would be reasonably complex.
What is your level of electronics experience?