So it should use the HTML5 video if you have opted into YouTube's HTML5 trial. This will only be used for new articles, but I went ahead and re-published the article you linked.

Open a Web browser and navigate to the YouTube video that you want to embed in your Publisher Web page file. Click the "Share" button for the video and click "Embed." Select the HTML code snippet ...

Copy the code inside the "Embed Code" window and paste it into the HTML code of your site of blog where you want the video with the external links to appear.