The way these systems usually work, the call comes FROM the keypad/speakerphone at the gate, TO your home number. That's how it can recognize the DTMF and open the gate.

If the call were coming FROM his friends mobiles, TO Google Voice, how would the gate intercept the DTMF? Note that he says the group includes "the number," not "the numbers."

The original article states that it is possible to set up a system this way, such that anyone who calls gets in, but it is insecure.