Thank you for your post Frida. As you suggested, I have now tried moving the energia directory to ~/home/$USER but it gives the same result.
The icon which energia creates on the desktop is labelled as "Arduino IDE" and, as I say, points to an Arduino file.
I looked again at the instructions for installing Energia on Linux and saw that the command line call is "./energia &" . When this runs it puts up anther desktop icon which I edited to point to the energia executable. This does properly load Energia.
The original Arduino IDE icon seems to be some sort of Arduino integration which is not properly integrated, so I've deleted it.