The real issue is center of gravity of the bottle.
The center of gravity has to be under the table in order for the match to hold the bottle. Otherwise, the match simply tilts up and falls as shown at the beginning of the video. The added matches push back the attachment point for the string, so the bottle is hanging under table.
Swinging the bottle side to side does not affect the stability as shown at the end of the video. On the other hand, allowing the bottle swing forward so that the center gravity is no longer under the table causes it to fall.
