function user_activity_settings_submit($form_id, $form_values) {
  if (is_numeric($form_values['user_activity_pis']))      variable_set('user_activity_pis',      $form_values['user_activity_pis']);
  if (is_numeric($form_values['user_activity_logins']))   variable_set('user_activity_logins',   $form_values['user_activity_logins']);
  if (is_numeric($form_values['user_activity_pis']))      variable_set('user_activity_nodes',    $form_values['user_activity_nodes']);
  if (is_numeric($form_values['user_activity_comments'])) variable_set('user_activity_comments', $form_values['user_activity_comments']);
}

As user_activity_settings() calls system_settings_form(), that code is useless, as saving the submitted values in Drupal variables is already done by system_settings_form_submit().