If you look closely at the picture you will see that it is using optical encoders for the position feedback sensing.
Stepper motors are probably the best solution for this kind of X/Y table. It's not a big deal if the motors skip or slip steps, as long as it doesn't miss encoder steps used to keep track of the table's actual position.
This is a good application for an Arduino board. First get the encoders working well then move on to commanding the stepper motors.
Lefty