If the user has the Mass File Download Permissions (Admin) permission set, they will have restricted access to the settings in the "About Mass File Download Tab" except for the "Select List of Supported Objects" setting. This means they can only modify the "Select List of Supported Objects" setting and cannot change any other settings.
The reason for this limitation is that the custom object where the settings are saved is accessible to users with the Mass File Download Permissions (Admin) permission set. However, the remaining settings are stored in custom settings, which require the Customize Application permission.
Unfortunately, the Mass File Download Permissions (Admin) permission set does not include the Customize Application permission. As a result, users with the Mass File Download Permissions (Admin) permission set can only access and modify the "Select List of Supported Objects" setting.