Base on this.
Step by step:
On your remote server:
sudo wget -O /usr/local/bin/rsub https://raw.github.com/aurora/rmate/master/rmate
sudo chmod a+x /usr/local/bin/rsub
Just keep your ST3 editor open, and you can easily edit remote files with
rsub myfile.txt
EDIT: if you get "no such file or directory", it's because your /usr/local/bin is not in your PATH. Just add the directory to your path:
echo "export PATH=\"$PATH:/usr/local/bin\"" >> $HOME/.bashrc
Now just log off, log back in, and you'll be all set.