I have checked the assets panel in designer and the videos don’t appear there but I don’t think background video files are saved or appear in this panel by design? (not sure about that though). I’ve also checked out the list of similar topics but they mostly relate to images rather than BG video.
Thanks so much for posting about this issue. I was able to make a copy of your site and import it. Once it was imported, I was able to export without any files missing. I sent those files to you in a DM.
There are a few factors which could cause this, your internet connection, ISP (internet service provider) issues, older browser versions, browser extensions, or of course a bug.