Thank you for the images. It is now clear that this is an earlier model, 2nd or 3rd generation.
The settings are in almost the same location:
(Apple TV A1378, A1427, or A1469:) Settings﹥AirPlay﹥Conference Room Display﹥Off|On
The Menu button should get you out of the screen saver.
If the remote is not responsive, then it may need to be linked to the Apple TV box again:
If your Apple TV remote isn’t working - Apple Support (2nd half of the page)
1. Unlink your Apple Remote to your Apple TV. On your Apple Remote, hold down Menu and Left for six seconds. Then on your Apple TV, look for 





above an icon of a remote.
2. Link your Apple Remote to your Apple TV. On your Apple Remote, hold down Menu and Right for six seconds. Then on your Apple TV, look for 
above an icon of a remote.
3. Unplug your Apple TV from the wall power outlet. Wait at least six seconds, then plug it back in.
Do both step 1 and step 2: first the unlinking, and then the linking.