Well…outside of the fact that you’re unable to load PHP in *.html files, let’s try to look at this from a different angle here…
One way that this could be done would be to convert all of the *.html pages – that you would like to include the news ticker on – to *.php pages, and to insert a PHP function that loads WordPress in the header of those files, along with the news ticker shortcode or display function.
Another way that this could be done would be to create one .php file in the root of your WordPress installation that only includes the aforementioned PHP function that loads WordPress in the header of that one file, along with the news ticker shortcode or display function, and loading that on the html pages through an iFrame.
Here’s the function I referenced above:
To include WordPress in an external .php file, place the following code in the header of the file.