The BRIDLE they have chosen to show it with, is “cumbersome”, with the addition of a flash, and keepers for a full cheek snaffle.
But the “gag hanger” is not complicated or cumbersome…
The primary action of a gag bit is to shorten the distance between the poll and the bit when you pull on it. This is the same with with the traditional gag and this device.
The secondary action of the traditional gag is that it rotates the bit within the mouth (the part that was pointing forward points slightly downward when you pull on the rein). (Someone in another reply called this “torque”. but it isn’t torque, just rotation.) The “gag hanger” doesn’t do that.
I do not now how much difference that rotation makes. It probably depends on your horse, and why you are using a gag.
But you are definitely still getting the “lifting action”.
The third difference is that, in a traditional gag, the hole-through-the-bit prevents the small ring attached to the rein from sliding through the bit. In the “gag bit hanger” you pictured there does not seem to be anything preventing that ring from sliding through the bit (especially if you are using a bit with larger rings). I would be concerned that the “small ring” would slide through the bit ring, and “hang up” there, and then you would no longer have a gag action. Maybe if you adjusted it so the “small ring” was a couple in inches beyond the bit ring, that would not be a problem.
Personal anecdote. Many decades ago (1960s) my sister was riding a pony wo had a bit of a hard mouth, and liked to go fast. She was working on transitioning him from a pelham to a snaffle. She was on the Pony Club Games team, and the rules at the time said you could only use a snaffle. While I had never seen a gag bit in person, I had seen pictures and descriptions, and decided that was what she needed as an “emergency brake”. I rigged up something that worked similarly to the device above, in addition to the regular rein, to be her “emergency brake”. (I no longer remember exactly how I constricted it, but it didn’t have a ring that connected to the rein.) It worked as intended.