Reinstalling the demo is free through the "Download demo" option above.
To unlock the demo to the full game:
When you're signed in to your itch.io account, at the top of this page it should see "You own this game". You can click on the "Download" button there to download more files, including the license key that unlocks the full game. There are instructions in those files.
More Info:
You can also check your email for a purchase notification from itch.io, where there's more information about getting access to your purchased games, including a link to:
which is a good place to find downloads for any itch.io games you want to reinstall.