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First of all please see this video : http://www.youtube.com/watch?v=n0dkn4ZIQVg
I think there is ony one stepper motor -or servo- working in the mechanisim. But as you can see each flip counter works alone and separately.
It is not like classical counter mechanism like this : http://www.youtube.com/watch?v=rjWfIiaOFR4
How does it works?
As far as I can tell, you are asking how a "split-flap display" on things like the Flapit, the Smiirl Fliike, etc. works.
Some flip clocks -- "Retro Flip Clock", etc. -- use a single motor and a "carry gear mechanism" so they can only count forward and backward (or in some cases only forward) in sequential order.
The video you show seems to spin the 100s digit, the 10s digit, and the 1 digit independently of the other digits, like split-flap displays indicating arrivals and departures at airports and railway stations.
I suspect it is possible to have a mechanism with a total of one or two motors to independently select one at a time of a large number of letter/digit flip sections, and then flip that section an appropriate number of times, perhaps something like the way the Armatron somehow managed to control a bunch of joints with a total of one single motor.
However, in practice, my understanding is that such displays typically have a dedicated motor for each letter/digit. For example, Markus' split-flap display (via "Driving an 8-digit split flap display" ), Tom Lynch's split-flap display (via "Split flap display: if you can’t find it, built it" ), the "Signal-to-noise" mechanism, etc. each use a dedicated motor for each letter/digit section.
