I've researched this thoroughly for you, Colin, and I am convinced it is a file format/codec issue as I previously made reference to in this thread:

http://answers.websitex5.com/post/64781

The video on the home page didn't play for me either in IE10.  So I downloaded it to my PC, and converted it to MP4 with H.264 video encoding and AAC audio.  I then created a project in X5 and embedded the MP4 file on a page with autostart active,the control bar visible, and the option for fullscreen enabled.  I uploaded the project to a test area on my server.

When I viewed the uploaded webpage it functioned flawlessly, in both IE10 and Google Chrome.  Audio, video, streaming, autostart, control bar, fullscreen, all worked.

If you really want to stick with the .avi file format then unfortunately it will become increasingly difficult to ensure compatibility with all browsers.  Things are moving fast and HTML5 will soon be the new norm.  MP4 is widely used on major streaming sites such as YouTube.  On the other hand, the fact that IE10 refuses to play your original file, does, I feel, speak volumes.

Internet Explorer is still a popular browser, but it is no longer the dominant browser by a long shot, and this has actually been the case for a few years now:

http://www.w3schools.com/browsers/browsers_stats.asp

Nevertheless, we should all still design for compatibility across the widest range of devices possible, and the best way to ensure this with Website X5 is to use MP4 (which HTML5 supports by default), with a Flash fallback.  The X5 help file explains this in considerable detail (expand 'Reference: Commands in the General section):

http://help.websitex5.com/en/index.html?ogg_video.htm