At 1:14 mark you can clearly see the building is not finished. There are outside walls missing and the building is still under construction.
Here's a photo of New York building under construction
In the left the buildings have external elevator and cranes. On the right building, at the top, you can see that the crane is still there after all external wall are put in place. It's there to move heavy machines (like AC) to the top at the end (so when all air ducts are in place, power is moved to the top of the building and so on).
Regarding the comment about worker working in the middle of the night. It's New York, city that never sleeps. They were building this 24/7.