HTML 5 video not working in Paralax slider

The slider you see here: is called LayerSlider and comes from

My problem is, the client really wants an animation that can't be done with just moving layers like this. So I've created the animation as a simple video and inserted it into the slider using HTML 5 <video>. It works fine, except that it doesn't autoplay as it's set to do.

If I put the same code in the body of the page, just beneath the slider, the autoplay works just fine.

Because it came with a theme I purchased, I don't have direct access to their support. I have messaged them, as well as the theme's developer, and so far have gotten very little in the way of help. I just wondered if any of the great minds around here might have some ideas as to why it's not working? I appreciate ANY tips, ideas, thoughts, etc. Thanks.