That appears to be a BLDC (brushless DC) servo motor. That would indicate it is a 3 phase motor with a permanent magnet rotor. It MIGHT run on a sensorless vector VFD. But the real question is what is the rated voltage?
If the existing drive is working, it looks like it can be controlled by an analog signal from the CNC controller. Mach3 will output the analog signal when using the correct hardware that will output the analog signal.