Extensions installed as unpacked aren't updated automatically. To update the extension you should download it and click reload in the browser extension management page.

Go to the releases and download "ChromeExtension.zip". Extract it to a directory of your choosing. Choose somewhere you are okay with leaving it (you cannot delete it while it is installed).

1. Open the "Extensions" page (chrome://extensions/) in the browser and turn on the "Developer mode".

2. Click on the "Load unpacked" button and select the directory you extracted the zip to.

Instructions taken from https://github.com/web-scrobbler/web-scrobbler/wiki/Install-an-unpacked-extension