I, too, have wondered about the technical details when I see stories like this. If the data was originally stored in S3, they probably used the Cloud Storage Transfer Service (https://cloud.google.com/storage/transfer/). The secret sauce appears to be parallelization of the transfers.
When I copied hundreds of GB of data from one bucket of to another AWS bucket, it took me days to do! Then I realized it was because I was running a single threaded process. The slowest part was getting the list of objects to copy. If I had a separate, faster index of the objects, then I could have done a copy in parallel much more quickly and max out the bandwidth available to me. (Maybe that is part of the rationale of Netflix's S3mper?).
I'm curious to hear other thoughts on accomplishing fast transfers of S3 data.
Edit: theoretically speaking, if you had 1 TB of data to transfer, and a paltry 100 Mbps (12.5 MB/s) connection, you could do this in under 24 hours if the entire network was fully utilized. Not a network engineer so go easy on me if I am wrong!
As for costs, sending 1 TB out will cost $90,000 in S3 transfer costs, before any other discounts.