For file folder structure, you seem to have things setup correctly, each sub-folder containing an instance of WordPress.
Following that, each instance of WordPress requires a separate mysql database and wp-config.php setup.
Can you confirm that the database and wp-config.php setup is separate from the main site?
Was the demo site an exact replicate of your main site? If so, maybe you need to do a find and replace command in mysql to change myexistingdomain.com to myexistingdomain.com/demo1

If you can supply some specific links I can look into it further.

Hope that helps ??
If you have any follow up questions feel free to ask!

Thanks
Jordan