It is clearly a counter (I had a similar counter as a kid, made in plastic and not pencil mounted). It is probably for counting something (inventory, people, …) while also taking notes with the pencil. I doubt that it is for counting the writing per se.
The only thing about this device that I think is unusual is the fact that there is no 1’s place. Just 10, 100, and 1000. Also the order of the place-values is reversed from their usual right-to-left orientation. The latter seems more like a design simplicity issue, but the absence of a 1’s place is strange. Why would the designer explicitly be thinking you’d be counting in tens and not ones with this thing?
It counts by 10s rather than by 1s (that is, the low order digit, which is on the left, not the right) is labeled 10. The picture does not provide enough information to tell whether it is counting up or down (we’d need to see the order of the digits on the wheels).
It looks like a perfectly ordinary design for mechanical counter, so I’m not seeing anything to get excited about—you’ll have to tell us what is so special.
If you look more closely at Fig 3, you can see that one of the pins on gear a (the central gear) is longer than the others (it happens to be the one engaged with the rightmost gear in the picture), the shorter pins will not advance the right gear at all.