I tested https://plus.google.com/hangouts/_/UNIQUE_HANGOUT_ID?gid=APP_ID
this evening, and it worked correctly - placing the person in the same hangout and running the correct app.
Is the app in question public? If not, this may be the cause of the problem.
As an aside, the https://hangoutsapi.talkgadget.google.com/
is now deprecated, since it was related to the old Hangout Development Sandbox which is no longer in use.