No, that was not it. These were not backups of my backups.

I did identify the issue - I was backing my data up using the CloudBerry 6.1.x and restoring on my older test PC where had previous installed CloudBerry Backup 5.7.3.

I installed CloudBerry Backup 6.1.3.9 on my test PC (this now matches the PC being backed up) and it worked. No more weird folder structure. I should have double checked version numbers.

No, I don't know how to copy.
I'm using the Restore plan / wizard. I select my AWS S3 account (using same access key used on the PC data was backed up from).
Below is the the summary of the restore plan. The back path on the original PC is "C:\Users\cvach\Desktop\No Backup\BCP" NOT "\\T430\C$\Users\cvach\Desktop\No Backup\BCP" as displayed in the Restore portion below (not sure if this matters).

Also when adding the AWS S3 account I chose in the advanced settings menu I chose "restore only" (but also tried "Regular mode" and selected the same backup prefix. Both ways yield the same end result.

Restore plan summary
Run restore once
Bucket name: XXXX-test
Backup prefix: DESKTOP-IKU0I31
Restore Type: Latest version
Restore:
\\T430\C$\Users\cvach\Desktop\No Backup\BCP

Destination folder:
C:\Users\T430\Desktop\delete\DR_TEST
Encryption: disabled

Notification options:
never send email notification

After running this restore plan on my test PC it placed the file in "C:\Users\T430\Desktop\delete\DR_TEST\BCP\Pictures\Lily.JPG$\20140215002812"