If you go to https://itch.io/my-purchases you can find Beam Saber in your collection and click download. This will take you to a page that has all of the Beam Saber files for download. The Playbooks are in "Squad Playbooks.zip" and "Pilot Playbooks V1.2.zip"
Alternatively, if you go to https://austin-ramsay.itch.io/beamsaber there will probably be a banner at the top saying "You own this game" with a download link below it.
Hope that helps!