Finally, figured it out! To set the minimum user role you need to edit the following file:
wp-pro-quiz/lib/helper/WpProQuiz_Helper_Upgrade.php
Change line 35 and 58 where it says $role = get_role(‘administrator’); from ‘administrator’ to ‘editor’.
If you already have the plugin installed and you make this change in the code, make sure to deactivate and reactivate it.