YouTube has Schema.org automatically applied. So do you need to add Schema.org markup to YouTube videos which you embed on your website? First, if you do not understand how Schema.org influences search you should read this article.
Matt Cutt’s from Google says, YES, please add Schema.org markup for to videos which are added to your website, even if they are YouTube videos. Generally, the more markup there is the easier it is for search engines. Also, it is important to allow Google to crawl the Javascript and CSS on your pages so that they can understand the entire picture.