Short range wireless pulse transmission in wind anemometer
I'd probably start by thinking about Hall effect sensors on the fixed part.  A single fixed magnet on the rotating part can then be used to find direction.  Or, use a shaft encoder for direction.

Presumably the impeller drives a small permanent magnet generator.  You could have this drive a coil that is sensed by another Hall device at the center of rotation.

How was this anemometer supposed to work in the first place?  It looks like a manufactured unit.  The manufacturer must have provided a way to get the data out.  Why can't you use whatever that is?

I once worked on a device that had to get about 90 W of power plus one-way communication across a rotating interface.  We used a rotary transformer to transfer the power, and light to send data up the hollow shaft in the middle.  These things can be done, but I don't recommend something so complex for a simple anemometer.