@andrealmc: I am not familiar with the Viking G5 Gate Controller, if you can provide more details or vendor’s link of User Manual, I might be able to tell in more specific.
But the snapshot you attached can also tell something. My suggestion is wiring NO(or NC)/COM2 of GDS3710 to “Fire/GND” in the Viking. And enable DTMF open door in the configuration of GDS3710, and configure special feature in GXV3275 so you can see and press the soft button in the video phone to open the door.
Where using NO/COM2 or NC/COM2, you can test connection with the Viking, see which connection works.
The GDS3710 will send out voltage via its built-in relay in NO/NC/COM2 socket combination, once it received open door command via: RFIC card, Local PIN via keypad, Remote PIN via SIP Call, or some Alarm_In hard signal via a open door switch, or 3rd party Weigand interface. There should be one falling in to your case.
Hope this helps. Please advise whether this works. Good luck and thank you for using GDS3710!