You have one or two problems ...

a) You stated you changed the define, but what you posted includes extra spaces around the double-quote mark, which would cause a problem.
b) It's very possible that the computer/server you're running it on doesn't even have the mysqldump binary/executable file on it. If you know that it does, you could try editing the /admin/includes/languages/english/backup_mysql.php file and set the actual path to it (instructions in the file). If it doesn't have the program on the server, then ... you can't use this addon until you install the mysql programs.