load node_type_form form
node_type_form() lives in modules/node/content_types.inc, which the system only includes when it needs to (to fulfil menu paths etc).

If you include it manually before your call to drupal_get_form() it should work...

module_load_include('inc', 'node', 'content_types');
$form = drupal_get_form("node_type_form");
// ...