Now, I get that a lot of people wouldn't know about all the different parts of a crane. But that's the lifting slings that broke. It would have been significantly more catastrophic if it had been the main cable, and the big block of steel, the main hook block, would have been on the ground.
My pet theory is the slings weren't being inspected frequently enough. You can see there's 2 slings, and the hook loops on one end snapped. Seeing as these are structural beams with a fair bit of length, those slings would have been in a choker or vertical hitch. Choker being wrapped around and one end passed through the loop on the other and then attached to the hook. Vertical hitch would require a anchor point on the beams.
Watching the video again, it looks like multiple slings looped together and then used in a tandem double choke. I personally wouldn't have done that, as two slings looped together are no where near as strong as a single longer sling. Whoever rigged that lift f**ked it pretty badly. But at the end of the day blame will most likely be spread around as the equipment wasn't likely being inspected frequently enough, or well enough.

Thanks for coming to my TEDtalk.