All I can say is "a Cheater rein on a pelham " at that level, REALLY?????
Often at that level it is harder to ride with two reins than a converter, and the second rein can get confusing when there is a running martingale in the mix. There is nothing wrong with a converter if the horse goes well in it.
If you read Dyon's explanation, it's all about keeping the crown piece well behind the ears. So second throat latch is actually a tad tight on the jaw and the redundant noseband attaches to it on the underside of the jaw.
Really, the Dyon explanation and pics do a better job than I can.
That is the most unusual configuration I have ever seen, and I've seen some weird ones. It looks like it could be a "jerryrigged" version of the Dyon, perhaps?
I'm not sure...the leather color and stitching look so well matched that I think it might be one bridle. Plus both throat latches and both crown pieces are connected. I'm thinking there is probably more to the bridle than we can see under the horse's chin and throat?