Then when double clicking the file the mail client (Windows Live Mail) would open with the email in the Inbox. Old Outlook clients worked the same way. I've had this working AOK with Windows 7 for some time.
With the same scenario under Windows 8 the Windows Live Mail client opens but the email is no where to be found.
The file association is AOK: .eml = Windows Live Mail (from File "Set Associations" screen).
Even just saving the email to a file from the client (Windows Live Mail) and then immediately trying to select it again does not work (after deleting the original email from the client).
Double clicking the file will open the file. It will not be in the Inbox.
Windows Live Mail will be partially running. Access to Windows Live Mail will require starting Windows Live Mail with the shortcut.