In the Slider Is there a Way to Place a video embed code or video short code instead of pictures
Can you verify if this works for you or not?
I was able to replicate the problem Chrome, but I didn't ask what browser you were using.
If this is good with you, I've made a shortcode that will make this much easier for you.
[youtube url="YOUTUBEURL" width="840" height="523"]
You'll need to update your theme if you want this to work.
I've added this to the repository if you want to download.
The only file changed was: wp-content/themes/functions/content_functions.php