I'd like to see the actual report from energy/cost saving. Too many moving parts to maintain. I am afraid just like everything else in UAE, you only see the polished side of thing, which is maintain by high cost.
The glasses get heated up to 90 C. That's almost boiling temperature- if the outer shell of the building is that hot, air conditioning will cost a literal fortune. Reducing that by half, and powering some motors for a few seconds each every day should be BY FAR less costly than keeping those monstrous towers cool. My experience as an Arch student has taught me that usually, going eco-friendly is the cheapest option to maintain. (Eco friendly systems are hella expensive to build, but they pay off in the long run).
I don't think they said it is inspired by nature. It is actually inspired by tradition. This mechanism is based on the mashrabiya, a type of latticework commonly used in traditional Arabian buildings for shading.