In screenshot you provided you set the run mode of the trigger to Publish. When you set the run mode to Publish that means that workflow will on be kicked off on a server that includes the Publish run mode. Since you author server has a run mode of Author that workflow trigger will never start a workflow - regardless of where you delete the page.
If you set up the same launcher on a publish instance it would would start a workflow - but only on the publish server - not on the author server. You probably want the to set the run mode to Author not Publish. Try that and you should see the results you expect (assuming of course that the delete action is happening on the author server and not on the publish server).