Apple TV no pictures from iMac only sound

My question somehow ended up in "OSX Mavericks", so here it is again, hopefully in El Capitan.

iMac 5K, 10.11.3, Apple TV 2, Software 6.2.1

I have no problems using Apple TV from my iPad or my MacBook Air (Yosemite 10.10.5) but it does not work with my iMac. Sound but no display.

I made sure the firewall does not block any communication but whatever I tried - no picture. I also tried Safari iso Chrome, same thing.