Unfortunately WordPress, unlike Joomla!, does not provide a fine grained permissions system. We have to hardcode the mapping between WordPress capabilities to backup software privileges. This is done in wp-content/plugins/akeebabackupwp/Solo/Application/WordpressUserPrivileges.php. Changing the mapping would require modifying that file. That said and according to WordPress' documentation
the Editors don't have the privileges you say they do but they can
If the user has the activate_plugins capability they are given Configure and Download privileges. Per the documentation, only Administrator and Network Administrator have that capability. These privileges allow the user to view and modify the configuration, as well as download and restore backups.
If the user has the edit_others_posts capability they are given the Backup privilege. Per the documentation, only Editors, Administrators and Network Administrators have that capability. These privileges allow the user to take backups but NOT view/modify the configuration or download/restore backups.
If the user is a super user (per WordPress' is_super_user() function) all privileges are granted.
Finally, if you are inside a multisite installation -therefore not a network administrator- you are stripped of all privileges i.e. you can't do anything with Akeeba Backup.