In your case $registered
is the user id not the user object so it does not work. Please use the code as given below.
add_action( 'user_register', 'set_user_registration_date', 10, 1 );
function set_user_registration_date( $user_id ) {
$user = get_userdata ( $user_id );
// Update the registration meta data
update_user_meta ( $user_id, 'registration_date', $user->user_registered );
}