If you log in as a non-root user into your graphical desktop environment after boot-up, you should be able to run gtk-gnutella normally from the command line.

Gtk-gnutella will refuse to run under user root, because it was not written to be secure. This does not mean, it is known to be insecure, but it means, that the developers don't want to be liable for any harm done by the programm and do strongly disencourage to run it under root.

The message "cannot open display: :0.0" probably means, that you either don't have an X server running on your machine, or that you for some reason don't have access to it. I assume the first, because in the latter case it should have printed something like "... blah not authorized blah ...".

Gtk-gnutella requires an X server as it has a graphical user interface.