Can I drive and reverse this motor with an ESC?
Yes, the ESC you bought will drive the motor. The motor is 3 phase BLDC.

The only problem you may have is that the ESC is low torque startup (it's designed for a Heli/quad copter. However given the large 10:1 gearbox you may be ok. 
If you need high torque at low starting speeds you really need a BLDC with Hall Effect position sensors

To add from your comment...the new controller you selected is exactly correct for your motor....which already has the Hall Effect sensors fitted.