I may be wrong, and if so, please someone correct me, and I am just guessing here
I THINK it might be what my trainer called a "rhythm collector". It is only very losely attached over the poll, over the back, between the fore legs and snapped to the bridle rings. The snaps, with every single step will give a small impulse on the bit on each side. In rhythm with the horse's steps. It is losely tied and the horse can move the head freely up, down or flexed. Due to the really minimal impulse by its own weight on the bits though with each step (gravity helps here), the horse is encouraged to find and stay in rhythm and balance out of its own volition. There is nothing on there, that pulls or tweaks the horse, or pushes the horse more clearly into a frame like side reins.
I have only seen those things once and they were attached to the horse at that point. I have no idea whether that's what they look like, once they are not attached to the horse, but with the snaps where they are, that would be my (admittedly quite uneducated) guess
Edit: I think Bluey is right. The stuff I was talking about is NOT trussing a horse up like that *lol* "Trussing it up like a Turkey" - Funny expression ... (for my own and my horse's safety, I'd never use those. I'm a klutz! I'd roll up in those like a trussed up turkey myself and hurt myself and anything attached to those :P )
I'm in the 'rhythm collector' camp too. The odd thing, when I looked at the photo, my first thought was the thing which is used on TWH's in their stall, to keep them, ahem, 'collected'. Not as tight, but in the same family, I would think.