Once there is a game update, the ‘server’ version will be updated as well. However the actual Patreon subscription is required to access it. You can return to this page and reinstall your game the same way: press ‘Play’, follow the link and wait until your game is updated in the browser. After that the new version will be available for offline play again.
UPD: since v1.8.0.5 once the version update is available the app will show the ‘<‘ badge right side. Click it for quick access to the ‘download’ page.