Reading about ping pong ball anemometers I discovered that the Mars Phoenix Lander had an anemometer of this design, and there are images and GIFs of it moving. When imaged from one or two different angles, it gives an estimate of wind velocity and direction. But imaging is a lot of bandwidth and memory (especially back then).
There was also a LIDAR instrument, but I don't know how demanding it was for power, or bandwidth, and if it could be pointed in at least a few directions fast enough to establish the direction of the wind, nor do I know if the direction was important.
After reading Wikipedia's article on Phoenix's Meteorological station I get the idea that they were looking for times when the wind was minimal, so that they could do sample loading without losing the smallest particles due to wind.
Wouldn't a hot-wire anemometer have used much less bandwidth and been easier to read? I think that as long as the air temperature is measured approximately, and certainly the pressure would be available from the weather station, this should work fine.
Also this looks a bit on the heavy side for a payload to Mars, compared to a hot wire, but that's just my perception.
above: Instrument as delivered to NASA. From the The Telltale project page on the Mars Simulation Laboratory. Also archived here. That's a 45 degree mirror below the telltale providing a simultaneous view from below.