The scene is pretty clear to me. The video starts with the falling debris from a close in intercept at the end of an exhaust trail (Patriot missile #1). We also see, at the start, the outward track of a second Patriot still in boost phase (you an see the bright dot from the missile exhaust)(Patriot #2). Then you see the launch of a third patriot, which immediately steers right after launch onto the intercept course. Partriots #2 and #3 burn out and we see nothing from time 14 seconds to time 22 seconds. Then we see a bright flash, which is presumably the intercept by Patriot #2 of its target, then we see a bit later a much brighter flash still, which is the intercept of Patriot #3, presumably much closer than the intercept of Patriot #2 given relative launch times, burst times and relative brightness.
I think that the presumption is that the three intercepts were successful since we see no further evidence of a still incoming warhead AND there is no attempt to launch another Patriot - which would be doctrine if one of the further out intercepts missed its target.
Third video down shows one of the missiles outbound then it does a u-turn and impacts and sends burning missile fuel into the air very close to the launcher. I think this is what is being seen as the very first video is starting.......