The <video> is an html5 element for embedding a video into an html document. This is not a link. The browser knows how to handle this tag (show video / add "download" item to context menu). Since this is not a link ( syntactically - as a tag - semantically , it is, of course, a link), there is nothing to hide, and nothing to show in the status line. Although, if desired, the developer, of course, the browser can do it.
if we talk about "how to hide a link to download from the menu": if you right-click on the youtube video, you will see that there is an item "about html5 player", which, in fact, is js / html strapping around the tag, intercepting the context menu (transparent div over video, for example), issuing your own menu, etc. You can google it further - for example - http://videojs.com/