No that chip drives bipolar motors and that's a unipolar motor. There are lots of designs for driving unipolar motors. If you know microcontroller programming, you can put a driver together for fairly cheap - ULN2003 plus a small uC.
Note, on some motors, you might be able to seperate the unipolar wiring to get a bipolar stepper. Do you have this motor already? If so, take a look at the connector. I think its a 5 wire motor so it may not be possible. If not, I'd go salvage one from a broken (and free) printer. Laser printers are a nice source of lots of scrounged parts.
I love the motor's datasheet - number one feature is "high torque output". who are they kidding??