Failed opening install.inc' when upgrading Drupal 7.x core with Drush 7.x
I managed to get it fixed after tracking the issue in drush 7, this is caused as you said by trying to load install.inc as Drupal 8 folder structure while you have Drupla 7 structure

I simply modified DRUSH_ROOT/commands/core/core.drush.inc line 1120

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


to be like 

require_once DRUPAL_ROOT . '/includes/install.inc';


I hope this help you.