Actually, I realize that I didn't properly answer the question: You said "without using a microcontroller."
No, you cannot control a motor controller directly from a PS/2 controller without using a microcontroller in the middle. You need a microcontroller to read the SPI data from the PS/2 controller, and write proper control signals to the motor controllers.
The closest you may be able to come would be to use a motor controller with built-in microcontroller, like the Orangutan from Pololu. But you're probably better off just using a motor controller (or motor shield) and an Arduino Uno.