Those error logs don't appear to have anything to do with the backup.

You are on a local server. Windows/Unix? What LAMP environment?

Add &debug=ON to the url and refresh the page, you'll see the list of places where the script is trying (and failing) to find the mysql tools.

You'll need to add the correct location on your server to the list in $pathsearch at line 254 \zc_plugins\BackupMySQL\v2.0.0\admin\backup_mysql.php