Close other user’s app
You cannot control processes you do not own as a non-admin user. If you can run the command as an admin, you can send the quit signal using the killall command for all existing instances of the program and quit the program that way. If you only wish to quit specific program instances you will need a more complex combination of commands. 

Granting selective admin rights to non-admin  users is possible, but keep in mind that granting process killing rights is universal and the semi-admin user will be able to kill any process. Shell scripting, AppleScript and Automator all derive their access from the same user privileges controls, so using a different tool won’t grant this right in a different way.