Interesting! I wonder what the difference is.
Edit: On Chromium, "https://" or "http://" I get served HTML5.
So, could it be that Firefox somehow doesn't provide the proper cookie value telling the site to use HTML5 when using "https://" (I did set HTML5 pref with "https://")?
Edit: A cookie named "GED_PLAYLIST_ACTIVITY", used for "[e]ncrypted connections only", is used on Firefox only. I don't see this cookie on Chromium on an encrypted connection. So, there might be a link with the presence of this cookie and the serving of Flash-based videos.