I don't think that this is a subject that has previously been addressed here.
All vending and affixing machines needed to advance the stamp coil the correct distance of one stamp. Below is an example from a Schermack vending machine. This is just one of many methods that were used and this may not be the type that was used on your stamp. Hopefully this will explain the concept better.

When the handle wqs turned the feed gripper would rotate counterclockwise over the pressure wheel advancing the stamp coil. A cutter blade (not shown) would cut the stamp from the coil allowing it to slide down the chute to a tray. The feed gripper had serrated teeth to engae on the stamp to ensure that it advanced the proper distance. What you see on your stamp is the impression left by these serrations.
Schermack also used a design with cam actuated serrated fingers that also produced a similar impression. Brinkerhoff also produced vending machines using a serrated wheel to feed the stamps. Other companys also produced vending machines but I don't know the specifics of their design.
I hope this helps in understanding the gripper marks.