I just opened quicktime to record some audio off a mic and notice all my apple TVs on the lan popped up as sources in quicktime. Naturally I got distracted from what I was doing and set it up. The message "do you want to allow screen sharing" popped up on the apple tv... click yes ... (duh might be an appropriate button ;) ) and proceeded to record myself playing PS4 games.
so now I have a quicktime preview window showing the apple TV in all it's glory on the mac, I open OBS and a new source, choose window source, and pick quicktime movie recording ... and there it is, full screen in OBS.
quality .... I'll get back to ya on that one but it looks pretty good so far!