Yeah, it is to collect water. Such that the moisture won’t run off down the side of the mountain. With the water from precipitation collected in the holes the land will gradually become more moist. And vegetation will be able to grow.
I was thinking water collection, or drying out something.
As a “counting” system, it doesn’t really seem practical.
Brian Foerester has a short Youtube video on this site and you can see there is a river not even a mile away. I have no idea what they were doing here but aliens and tribute-measuring both seem unlikely.