During troubleshooting on a couple of different devices and browsers, I noticed that the issue of the missing styles only appears when visiting the 'Gatherings' page as a logged-in administrator.
When the same page is visited as a guest (i.e. non-logged-in visitor), the styles are loaded correctly.
The core of the issue is that for the logged-in admin users, the following CSS file from the active theme is not loaded:
{yourwebsite.com}/wp-content/themes/salient/css/build/elements/element-video-lightbox.css
As a quick workaround, I've included the following code in the 'Output Editor' section of the view 'All Videos', which loads this missing CSS files for all users:
For a proper fix, I'll recommend getting in touch with the theme author, to better understand why this particular file is not being included for the logged-in users.