No, now that we know that OP's inbound did not even arrive at its gate until T-13 ("arrive" means brakes locked"), it is physically impossible for OP to have been at the departure gate by T-15. Even presuming that it only took OP 5 minutes from the time the brakes locked, the jet bridge was connected, and he deplaned and walked to the next gate, that is still T-8.
The GA quite properly UG'd another pax into the seat for which OP misconnected. And, now that we know that the GA had 7 minutes to do that, it is hardly surprising that this ocurred.