While everything is working with the local web server, your HTML documentation hosted on GitHub and served as a GitHub pages has a broken or indefinitely loading table of contents.
By default, GitHub assumes that you are hosting Jekyll (a static site generator) compatible pages: file names starting with a "_" (underscore) are ignored and not served by the GitHub web server. However, HelpNDoc generates files starting with a "_" (table of contents, keywords...) and those files are needed for the default HTML template to work correctly.
The solution is to include a .nojekyll file in the root path of your HTML documentation to turn off Jekyll on GitHub pages. See this article from GitHub for more information.