I think you can just run the program from the extracted tarball. A member on our Community site has put together an extensive manual on how to install this program to your system in such a way that it is also added to your menu and such. See here: http://community.linuxmint.com/tutorial/view/907. If you are on Linux Mint MATE, note that you should replace the "gksu gedit" part of commands with "gksu pluma". If you are on Linux Mint KDE, that would instead be "kdesu kate".
This is where I run into problems, it appears the tutorial is attempting to move a file here (as super user) but I cannot see a destination folder for where we wish move the file
Well, I think it is renaming first the directory "Sublime Text 2" to sublime. Then that directory sublime is moved to /opt. /opt is in the root of your filesystem.