The docs specify that php -S <port> starts a basic web server. Is there a way to stop this other than manually killing the process (kill -9 PID) ?
Ctrl+C will do the job. This you also can find in the docs.
No there is no other way if daemon is detached from terminal. Linux start/stop scripts do same: they kill processes.
When you run daemon it saves info about process into /var/run/your_daemon_name.pid file. Start/stop script knows that your_daemon saves its PID (Process ID) into your_daemon_name.pid file. So it do someting like:
kill `cat /var/run/your_daemon_name.pid`