Yup, I posted the original comment to quickly, the airflow indeed also pushes the brass disk forward, thus rotating the fan! An extremely clever solution that seems to be very easy and cheap to manufacture.
> the airflow indeed also pushes the brass disk forward
The force on the disk is caused by an opposite force on the fan blades, cancelling them out (since they are connected by the frame and the bearings), so it cannot cause the fan to rotate.
The rotation is due simply to unbalanced thrust from the fan. The unimpeded side produces more thrust than the impeded side, so the fan turns to that side.
I think both effects are at work. Thought experiment/hypothesis: If you detached the plate and merely held it in front of the fan blades, I think the fan would still rotate due to the decreased airflow on one side of the fan, but it would rotate less quickly since the force that moving air is applying to the plate would no longer be acting on the fan.