Oh, it does. It's just that it doesn't prompt me for which file to download. I actually have to install the demo first before I am able to manage the installation to also download other files. Which I don't usually think to look for, since the other files are usually versions for other OSes or earlier versions of the game, not supplementary files.
I think you could reduce confusion by calling it something other than Demo. Though I don't really have a good suggestion for what to call it, since this isn't a common method of distribution.