Clearly the teeth are part of a ratchet system that controls the carousel and moves it around.
However the problem is complicated by the fact that in Mr PM’s photo the long horizontal lever, at the top of the door, is missing, as is the ratchet lifting arm that drops down from it to the right hand side of the toothed wheel. Also missing in your (Scottie's) photo, I think, is a connecting link goes to from the above horizontal lever to the small lever in the top of the coin chute.
I think that as the coin drops in the chute it lowers the horizontal lever thus lifting the drop arm to ratchet the toothed wheel around one tooth so that the coin can fall into an empty slot in the carousel.
On Mr PM’s photos the horizontal bar that runs across immediately above the carousel is missing on your (Scottie's) photo. I think this bar acts as a backstop for the toothed wheel ratchet and plays a part in the pay-out mechanism by moving the drop arm away from the toothed wheel so allowing the carousel to drop back one slot and effect a pay-out. There is a pin on the back of the horizontal bar and the drop arm's bracket is slotted for this to happen.
If you look closely at Mr PM’s top two photos you will see that there are two other missing teeth; one at the top where the coins enter the carousel from the coin chute and one at the bottom just to the right of the weight.
I think the reason for the missing tooth next to the weight is that when all the slots are full the carousel needs to stop with the bypass coin chute aligned, so the coins go into the cash box, without the drop arm continually trying to drive the toothed wheel around. A missing tooth is a very simple way to achieve this. The other two gaps, I think, are also do with stopping the carousel at ether end of its travel and / or for effecting a pay-out but without being able to see the mech. behind the aluminium carousel cover I can't be sure..
Apologies for the overlong explanation but I hope this helps.