Hey
I have downloaded the 32-bit tarball for Linux - Elementary OS freya/Ubuntu 14.04 build
Since it is not a deb package, like previously, how to upgrade ST2 to ST3?
Simply clicking the executable file opens the editor but it does not upgrade the existing package.
No it does not. It’s just the applications binary folder such as the portable version on windows which is packed as zip-file.
You can copy the folders content over the existing installation (I guess under /opt/sublime_text_3 or so) or you might use one of the linux installers provided via apt (see: https://www.sublimetext.com/docs/3/linux_repositories.html).
Tarballs are for manually installation. You can install it where ever you have the rights on your system. In your user directory , under /opt or /user/local.
If your linux distribution is one of the mayor ones than you could follow the advice from @deathaxe and use an repository that is suitable for your distribution.