Won't work on my system (4.7.10) and replicated on Wordpress sandbox.
I've created a very simple profile: last name & first name. All fields are expose publicly, searchable, results column etc Profile ticked "include profile edit links in search results?
Using link from profile "use - listings mode" while logged in as admin. Ie "http://wpmaster.demo.civicrm.org/civicrm/?page=CiviCRM&q=civicrm/profile&gid=14&reset=1"
Search works fine but listing only has view option - no edit
Same when using [civicrm component="profile" gid="68" mode="search" hijack="0"]
Am I missing something? Same setup works fine on Drupal site