I believe I am having the same problem. I have this setup:
- iPhone 6, model A1549, running 9.3.1 (13E328)
- Airport Express 802.11n 1st Generation, model A1264, running 7.6.4
- Apple TV 3rd Generation, model A1427, running 5.3 (6105)
I am trying to mirror my iPhone screen for a Keynote presentation. I believe that all are running the latest available software versions. The Airport Express is in there to create a WiFi network because I will be presenting at a venue with no WiFi, and it has no upstream internet connection.
I see my Apple TV in Airplay, but it shows up as a speaker instead of a display:
When I connect my iPhone to the Apple TV, my video does not mirror. I can only play audio through the Apple TV. I was hoping to use this setup for a presentation in a couple of days, but it looks like I will need to set up something else. Help!