There's the need for parameters to specify database username and password other than the ones in wp-config.php.

The --<field>=<value> syntax works for the password, but it fails for the user because the --user parameter is already taken to specify the WordPress user.

See here for more details.

I suggest to create new parameters, namely --dbuser and --dbpass and bind them to the --user and --password parameters of mysqldump respectively (albeit a new mapping for --password is not strictly required, but adding it nonetheless makes things cleaner).