There is no 'user setting'' for this but you can achieve it using QuizXpress skinning. A QuizXpress 'skin' is basically a set of assets (image files) and a large settings file (text/xml file) with all the defaults (colors, fonts etc) used in QuizXpress.
You can tweak this file to make the quiz player look like you want.
The default skin file can be found in the QuizXpress installation folder and is named 'skin.config'. To make the system use your custom skin, copy this file to the QuizXpress application data folder. You can open this data folder by pasting '%appdata%\QuizXpress' in the Windows Explorer address bar or from Studio, on the HOME tab, Advanced menu, Browse Datafolder. Note: do not edit the file in the installation folder itself as it will be overwritten when you install an update.
Once you have copied this file, you can edit it with your favorite XML editor. A very good free one is Notepad++ (https://notepad-plus-plus.org/downloads/).
Look for the section named <quizscreen>:
and change the 'background-image' attribute to point to a file with your background image or video. Now this image or video will be visible behind your quiz slides.