This package is tailor-made for use inside Laravel applications. But with a little bit of good will you can use it to backup non-Laravel applications as well.
To do so install Laravel on the same server where your non-Laravel application runs. In the Laravel app you'll have to install this package using the installation instructions. In the app/config/backup.phpconfiguration file specify the paths of the non-laravel application you wish to backup in the backup.source.files.include key.
Do not forget to configure the database as well. In app/config/databases.php put the credentials of the database used by the non-Laravel application.
When running php artisan backup:run on the command line, the application will be backed up.