Apple TV Remote iOS App Not Connecting to tv4

I can't seem to get the new Apple TV Remote iOS app to connect to my Apple TV 4th gen. As shown in the picture, the tv shows up on the screen but tapping on it gives ~10 secs of spinning gear and then the message:

Make sure "Apple TV" is turned on and connected to the same Wi-Fi network.

No problem playing audio/video from the iPhone to the tv using AirPlay, so they do connect with each other using that protocol.

One thing: the tv is connected to the network via ethernet (not wifi). The app does state "make sure they are connected to the same Wi-Fi network", but surely that should support ethernet connection to the same LAN as well. TCP/IP transport does not inform a device how other devices on the same LAN are connected, just that they are, or not.

Other info:

• iPhone 6 running iOS 10.2 (14C92)
• Bluetooth is on
• Apple TV Remote app version 1.0.2 (Sep 19, 2016) (latest per App Store)
• Apple TV 4 running tvOS 10.1 (14U593)