Yes, ST2 is only available as a tarfile which is similar to a windows "portable install". ST3 is available as a .deb for Ubuntu/Mint type distros and so should be an easier install.
If you're using ST2, you'll need to do some stuff yourself.
Don't extract Sublime on your desktop. It's better to install it somewhere in the system, or at least into your home directory. I have it installed into the following: ~(home)/dev/tools/sub/
Create a symlink to the executable somewhere in the path. I made a symlink /usr/local/bin/sub -> ~/dev/tools/sub/sublime_text. You'll need su/root to create a symlink there.
Then in Mint, you can right click, open with other application, click + on Use a custom command, then enter "sub" as your custom command. You can click "remember this application..." if you want to always open this type of file with sublime.
If you install ST3 from the .deb, it will probably do most of the above for you (can't say for certain as I've not installed ST3 under Linux). You'll also get nice integration with icons appearing in mint menu etc. But none of this bothers me personally.
The only thing that really annoys the hell outta me with ST under Linux is not being able to get rid of the sodding menu. Jps, when?!?!