Open root console and edit /usr/share/applications/gvim.desktop file. Find line containing Exec=gvim %F and replace it to the following:

Exec=gvim --servername GVIM --remote-tab %F

Now when you open file from Nautilus, this command will be run. If this command was launched before it and gvim instance is still running, new tab with specified file will be open in it.

If you want it to work in console as well, add this command to .bashrc:

alias gvim='gvim --servername GVIM --remote-tab'