I'm leaning towards it being part of the website. The video doesn't seem to play very often, but every time the page loads, there is a script tag from "vindicosuite.com" at the bottom, which contains links to specificmedia.com. Both of these domains are related to video advertisement.

To see the tag, I load the page in Chrome, rightclick->Inspect Element, and scroll to the bottom of the HTML view.

I see this both under Firefox on my laptop and Chrome on my office computer, it seems unlikely that they would both have the same malware at the same time.