On the top ring it is essentialy a hanging cheek snaffle. Very little poll pressure.
If your reins are connected only to the lowest ring then when you pull the reins the cheekpiece ring moves forward and drags the bridle downwards. This is your poll pressure and it is this which encourages the horse to lower his head.
However because the mouthpiece is on a separate sliding ring, once the mouthpiece reaches the end of it's sliding action and hits the cheekpiece ring this will make the horse lift his head (this is the gag action and why the bit is not dressage legal). Thus the bit becomes extremly confusing for the horse. Putting a 2nd rein on it (on the snaffle ring) helps to prevent the mouth piece from hitting the cheek piece ring all the time becuse you ride primarily on the top rein and thus helps to eliminate some of the confusion for the horse.
The middle ring has a similar action to the bottom ring except you have less leverage and thus less pinching action
I realy don't like the dutch gag as it is an extremely confusing bit in its action, it is generaly used by people who don't understand it (normaly because it has been described as a continental snaffle) and generaly haven't got the hands to handle it.
BTW the bit pictured above is not an elevator gag. The 3ring gag/4ring gag/dutch gag/passoa gag/continental snaffle is often mistaken for the elevator and it does have a similar action however the elevator has more leverage on the poll and more of a pinching action on the horses head.
This is an elevator