The embed code from YouTube contains an <iframe> tag which is like a web page within a web page. The iframe projects a dynamic page from the YouTube site on to your site.
This dynamic page contains the <video> tag.
Below is the embed code for Nyan Cat:
<iframe width="420" height="315" src="https://www.youtube.com/embed/QH2-TGUlwu4" frameborder="0" allowfullscreen></iframe>
If you open the page listed in the src attribute and search the HTML markup in the browser developer tools there is a <video> within the first few <div> tags.
<video class="video-stream html5-main-video" style="width: 670px; height: 317px; left: 0px; top: -317px; transform: none;" tabindex="-1"></video>