Does an outdoor outlet mounted on a patio ceiling require protection from a GFCI?
In my opinion (not AHJ). You don't need a GFCI on receptacles that:
1. Cannot be reached without the use of special equipment.
2. Are being used for a specific duty.

However, the receptacle shown is in a damp location and the cover that is on it not rated as such. It needs to be changed out with a weatherproof cover. If anyone is questioning why it is a damp location rather than wet. It's because rain or normal operation does not require it to be in direct contact with water.