It's possible...but some of those ways you can use this will kill page usability so be careful when configuring.
To start you need to make sure you have your dependencies covered for this thing, according to their doc they are..
jQuery (included by xf)
BigVideo.js (this plugin script)
Video.js (html5 video player this script uses)
jQUeryUI (can conflict with jQuery Tools which is used with xf, you can include the parts the script needs from jqUI or you can setup no conflict mode)
those would either need to be included in the head or at the end of the body (I haven't looked into this really so I can't tell you off the top of my head) and you would also need to setup like a configuration function so that bigvideo is initiated the way you want it to be.
I would think you also need to wrap the entire page within the body tag within a set of div tags to wrap it so that the contents of the body is sitting on top of that div in a stack...the video can be applied to the wrapping tags which give you a video for a page background.
I recommend you making a something.html document from scratch with a simple content box and see if you can setup the video background behind it there where it is much simpler and will actually help you grasp how it works.
Once you understand how the plugin works it will be much simpler for you to implement within an existing system which makes use of templates, inclusions and things of that nature which a standalone html file does not.