Yes, the problem is the WordPress version. Nothing earlier than 3.8.1 is supported. Your version of WordPress doesn't load jQuery automatically. However, we are not allowed to load it ourselves as this practice is incompatible with WordPress 3.5 (or 3.6, I am not perfectly sure) and later. That's what we were told when submitting our plugin to WordPress.org's plugins directory.
However, there is a trick to force-load jQuery on these old WP releases. Edit the file wp-content/plugins/akeebabackupwp/helpers/defines.php and append the following line:
Make sure that the files jquery.min.js and jquery.migrate.min.js are present in the directory wp-content/plugins/akeebabackupwp/app/media/js. If they are not present you can download them from jquery.com or just tell me and I'll send them to you.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!