The outputs on the Gecko drive look like they are open drain collector type.
With these outputs it should be possible to just connect them to the 3.3V TTL inputs at the DB15 port connection on the Integra (J10).
The inputs you can use on the DB15 port are at pins 9, 10, 12, 13, 14, 15.
Those input pins map to the P14 inputs in Mach4.
9 - P14 IN6
10 - P14 IN7
12 - P14 IN14
13 - P14 IN5
14 - P14 IN3
15 - P14 IN1
You can connect the GND from CN2 connector to pin 11 on the DB15 port.