How to load a file located in core/includes?
You can use a good old fashioned include_once (or require_once):

include_once DRUPAL_ROOT . '/core/includes/install.inc';


Core uses the same method any time it needs to source a file in core/includes. Case in point, ModuleHandler::loadInclude itself does exactly that if the file extension provided is "install":

public function loadInclude($module, $type, $name = NULL) {
  if ($type == 'install') {
    // Make sure the installation API is available
    include_once $this-&gt;root . '/core/includes/install.inc';
  }

  ...