I wonder what is the purpose of this executable, and is it necessary to have it running in the background all the time ? (even if it is a small memory consuming program)
Is it only necessary in order to launch Dopus with a double click from the desktop ??
Desktop double-click is the least of things that dopusrt.exe does. Just do a search for it on this site and you will see it used in hundreds of buttons people have created. Yes, it is necessary. Why would GPSoftware take the time to write something that isn't necessary?
dopusrt.exe can be used to send commands to Opus from other programs (or batch files, etc.).
The background process you see is purely for Desktop Double-Click. If you disable Desktop Double-Click in Preferences then you'll see that the process exits. Enable it again and the process comes back.
So if you don't use Desktop Double-Click just turn it off and the process will go away. It's very small, though, and usually uses a tiny amount of memory.