Unfortunately there is no way to access the photos on an AppleTV 2/3 that were being used as a screensaver.
The only photos stored in the cloud would be 'Photostream' photos for a particular iCloud identity use to take photos on an iPhone/iPad or imported to a suitably set up Mac/PC.
See:
http://www.apple.com/uk/icloud/features/photo-stream.html
I'm not cler about the Pictures Library aspect mentioned here i.e. does it just get updated with photos from an iOS device camera or are pictures imported in a PC in a particular way also added to Photostream.
Photostream is also limited in what it holds - I seem to recall it was the last 30 days photos but rarely use it myself.
What happened to the hard drive? Have you considered a commercial data recovery option, though it would undoubtedly be quite expensive.
Not sure if this would work:
https://www.grc.com/sr/spinrite.htm
I did actually buy years ago, but couldn't recover an old Maxtor drive with it. Unfortunately no demo but they offer a 30 day money back guarantee (I didn't bother as I though I might try it again in the future).
AC