Is it possible to transfer the games to my EHD (Western Digital Elements, 1TB) on my Cyberpower Win 8.1 PC?
It depends on what you backed up.
If you backed up the installers for the games, you can copy those wherever you want. Game installers from GOG will install and play. Game installers from Adventure Shop will install, but you'll need to activate them in order to play.
If you actually installed the games onto the "The Book" EHD using a different computer, it probably won't be much use to copy the install folders from the "The Book" EHD to the Cyberpower because anything that was installed into the registry on the old computer won't be on the "The Book" EHD.
If you're talking about Big Fish games, they'll need to be activated. They don't need registry entries to play, but they'll only play as demos on a different computer. You'll have to redownload them in order to activate them.