When you click on the play button and the video pop up loads, the browser gives warning that this page is trying to load scripts from unauthenticated sources.
Visit your website in Chrome,
click on this icon on the right in the address bar:
After clicking the icon:
in the little pop up click Load unsafe scripts (or it says something similar)
and your video pop up is going to work.
This is definitely not the solution yet, but you get a little closer what is happening right now…
What can you do?
Make sure you uploaded everything as provided by the author,
Read this article in Chrome help: Manage warnings about unsafe sites
And finally scroll to the end of the page and see “My site or software is marked dangerous” part, there is a link for site owners to request a review.
Furthermore it would need to dig a little deeper to find out what happens.
First of all:
I encourage you to set up a test site in a new folder with the original files uploaded and test it by changing only this part of your site and see if it works. It might give the answer how to proceed.