The show's hosts: Steve and Rick are both demonstrating drawing techniques for USPSA/IDPA competition, therefore their draws are subject to those sports's safety requirements i.e. disengaging/rengaging safeties when drawing. Steve (the 1st guy) is disengaging and reengaging the safety when he draws. It's more noticeable when he is simply practicing drawing than during the live fire demo.
As for Rick,
I'm not sure if he has an ambidextrous safety on his gun, but he is disengaging and reengaging the safety after every shot.
Glad you guys like the video, I've watched most of their episodes and I think they even post on here from time to time with new episodes.
To the OP and Mello2u, I agree that establishing a guard/second scan for other threats after shooting is important as well.
One thing that they do not do, that you can do when practicing, is after you fire; come to a guard position, scan for more threats, then holster without taking your eyes from looking downrange. You should learn to holster you weapon without looking at your holster.
I've definitely seen this ^^ before in IDPA competitions. (mostly by LEOs)