You probably don’t need to install anything unless neither of the commands work.
On Debian/Ubuntu, mariadb-dump/mysqldump is part of the mariadb-client package, which is a dependency of the mariadb-server package. So unless you deliberately uninstalled it, either of the commands should work out of the box.
I’m not sure about other distributions, but I assume it’s similar there.
Feel free to click the ‘Edit on GitHub’ link at the top right corner of the relevant documentation sections and open a pull request.
But to be honest, I don’t see any real need to update the documentation. The mysql commands work with both MySQL and MariaDB, whereas the mariadb commands only work with MariaDB. So anywhere the docs mention a mysql command, you’d have to either duplicate the instructions or at least mention both commands, which would be quite a bit of effort with no real benefit, in my opinion.