Note: You are currently viewing documentation for Moodle 2.9. Up-to-date documentation for the latest stable version of Moodle may be available here: Security FAQ.
Not sure how long it has been (at least Moodle 2.5) since it was changed however to enable ReCAPTCHA you need to go to:
Site administration > Plugins > Authentication > Manage authentication
... not ...
Site Administration > Users > Authentication > Manage authentication.
Please update the Security FAQ as there is no Authentication under Users.