The demo setup has as only purpose to get you started with Activiti in a matter of minutes.
Since we can't assume anything is installed on the machine (besides Java), we download it all to make it work on as many machines as possible.
Of course, this isn't the way you'll want to run Activiti. Since Activiti is a plain old Jar, you can do anything you want: run it in your webapp in Tomcat, Jboss, etc. Or run it standalone, with Swing, etc. The demo setup should give you enough insight in an example setup with Activiti, but it is surely not the only way to do it.