I don't know if it's available on macOS, but try right-clicking the video and see if there is an option to detach the display.
Thanks for the fast reply. But no, there's no such option. Just Close Display, and the usual options for Streams and Jump To and the like:
When a video goes full screen in MC on Mac (either by playing a video file, or opening Theatre View), the main MC UI disappears and a maximised video window appears on my chosen monitor.
Going into Mission Control (a Mac feature which displays every open window on the system, across all monitors. Maybe similar to Windows 10's new Task View) shows that there are two MC windows open, both on the display I've selected for video playback. One is the window showing the video, and the other is a completely black window. This black window is only shown when video is displayed full screen. Maybe it represents MC's video playback engine.
That's when I'm playing a video (Display View). When in Theatre View, things are slightly different. This time there are three windows on the monitor chosen for full screen display: the Theare View UI (window title: Theatre View GL), the same black window as before (window title: Media Center 24), and also a grey window (window title: J River Media Center 24).
But in both cases (Theatre View and Display View) the original UI window is always invisible and inaccessible - the monitor where it was before just shows the desktop, and it's not shown in Mission Control. It automatically reappears as soon as I go out of Display or Theatre View. I couldn't find any option that would change this and make them accessible simultaneously.