These people did arrive at the gate 10 min prior to scheduled departure time. Surely the GA could see in the computer that they had checked-in at the airport and the time stamp (meaning they might be heading to the gate but got held up in security or using the restroom, or whatever), so I'm not sure why he chose to close the flight early.

The rest of the story is obviously a very unpleasant learning experience for a novice traveler.