When I first bought Elgato Prompter, one of my main uses would be presenting online, sharing my main screen while looking at my Presenter notes on Elgato Prompter. This workflow stopped working after a Keynote update some time ago.
Just today, I found an unchecked box in Keynote's settings, Show presenter display window in other applications.
I went ahead and checked that box, and, voila, the Presenter Display is visible again in Elgato Prompter.
You'll see a detailed description if you hover over that checkbox's text.
Select to allow the presenter display window to be viewed in other applications when you share your screen.
What happens is that Elgato's teleprompter isn't like other monitors connected to your computer. It receives a "shared screen" from your Mac via DisplayLink Manager.
I hope this helps!