Reviewing the question and the video leads me to believe that I erred in my answer below. The photo of the cycloid gear threw me off in that direction.
I think the original question is answered by a detent mechanism, not a cycloid gear mechanism.
When one wishes to provide stops for rotation, a detent system is implemented. This can be as simple as a spring-loaded lever which engages a set of teeth on the gear, or can be more complex and more efficient by using a spring-loaded ball bearing engaging matching holes in the outer mechanism.
Many common devices use a detent system. Consider when a knob is rotated and clicks are felt. Within the control would be at least one ball and spring and a number of holes to accept the ball, around the rim.
EDIT: Portion below appears unrelated to original question.
It appears that the mechanism you seek may be known as a cycloid gear or cycloidal drive. The returns from my search using the first term add a line or two referencing the use of the device in clocks. I've noted that this device/mechanism has more parts than shown in your photo and as such, may require adaptation for your purposes.
I've found in the past that this device is also used for pumping fluids (air/water/etc) as the volume between lobes varies appropriately during rotation.