The steam demo button can be buggy. For example, if I have the game already owned and installed, that demo button doesn't do anything when clicked. And, when I have it just owned, it won't install the demo, it installs the full release version. So, it could be any number of things going wrong. It's tough for me to fix because I have zero control over how Steam manages that demo button click.
Are you clicking demo from the website or the Steam app? Have you restarted Steam? I'd suggest sending Steam a ticket/email if it continues to not work. They may be able to provide a solution.