The more I study this, the more I think the circled connection is just a switchable pass through and the signal isn't intercepted by the amp at all.
That would make sense because the TV has to get signals from the DVD and the Apple TV too. When I select a source on the remote, the amp selects an input to connect to the TV. The sound and video are separated by the TV and the sound is sent to the amp via the optical cable, since sound is all it needs. The amp has four or five of these ports (you can see them to the left of the cable IN wire in the image above), while the TV only has one or two, so to hooking up all three inputs (cable, apple TV, and DVD) to the TV would be impossible.
I'm at work now and can't get the make and model of the amp. Sorry.