Follow the instructions in that link dealing with Registry Key method.
The key you are looking for will not have many entries in it. And, in the section named "Title" will be named just as it currently is in the Game Explorer.
When you drop a shortcut into the Games Explorer, its assigned a number.
It is also stored in 2 places.
Location 1 is the Registry entry itself.
Deleting this key should remove the shortcut from the game Explorer.
To completely remove it delete the other folder it created.
Location 2 is actualy folder/shortcut itself.
C: /Users/ [User name] / AppData / Local / Microsoft / Windows / Game Explorer
The numbered folder will be the same as the numbered registry key.