I think what was going on was that SWA wanted the passengers to go to the check in counters to have their rebooking handled. The agents at the gates were trying to work other flights. That's fairly normal. I don't think that SWA has a customer service counter inside of security. The real problem was they didn't have any flights to rebook the passengers on.
No idea why it became a stand-off. That part isn't in the video. SWA called MNAA (Metro Nashville Airport Authority) for help and MNAA sent the officer who didn't handle it very well. Crowd control would be a function of MNAA but that's not how it's supposed to work out.