I don't know whether there is sth special with Cinnamon, but with LinuxMint Xfce using Twine is straight forward:
- checkout if you run 32bit or 64bit Linux
- Download appropriate Twine version from twinery.org
- unzip the download
- cd into twine_2.2.1 directory and call ./Twine on command line
==> a window with Twine will open
Of course one can use the online available Twine via the 'use it online' link on twinery org - story files will locate on your pc and *not* in the cloud. That one uses the browsers file space and needs some attention not to delete stories when resetting the browsers data.
I prefer the online Twine to checkout out code snippets immediately, while using the installed version for longterm projects.
I will add comments to steps 1 to 4 in a separate comment.
Hope, that helps a bit.