Note, updating Webshots does not remove saved pictures or playlists.
Click the "Click here to exit" text and the auto-update will install the new version.
Click on the "Windows" or "macOS" blue link.
That loads up the installer in your web browser. In Google Chrome you can see this in the lower left corner.
When it finishes, click that panel to finish installing. (You can also select "Open when done downloading"). When installing, the new version will uninstall the older version for you.
Then start the application using the Webshots shortcut on the desktop.