Pilot here: I'd bet you 100 bucks the Citation had the Southwest 737 in sight the entire time while on the approach, and knew exactly what was going on. There was almost certainly little to no danger of a collision. When on a visual approach like this you are literally watching the runway the entire time.

You can hear the Citation confirm and ask twice if they were still cleared to land, even after they were already cleared to land, so the Citation was gently nudging the controller that "hey, there's still an airplane on the runway."

It was a go around at the airport because of existing traffic on the runway. This happens all the time. Granted the controller got bogged down task wise, but the Citation knew it. I'd even bet you that the Alaska flight behind the Citation watched the whole thing go down with amusement.