has_header_video() │ WP 4.7.0

Check if the header video is there and if it should be displayed on the current page. If it's OK, we show the player with the video playing.

// check if there is a header video and it should show on the current page.
if( has_header_video() && is_header_video_active() ){
	the_custom_header_markup();
}

As a result, the HTML code of the video player will appear in place of this code, and the necessary scripts for the player will be connected to the page (to footer):

<div id="wp-custom-header" class="wp-custom-header">
	<video id="wp-custom-header-video" autoplay="" loop="" width="954" height="1300" src="http://example.com/wp-content/uploads/2017/01/polina.mp4"></video>
	<button type="button" id="wp-custom-header-video-button" class="wp-custom-header-video-button wp-custom-header-video-play">Pause</button>
</div>

Scripts in the footer:

<script type='text/javascript' src='http://example.com/wp-includes/js/wp-custom-header.min.js'></script>

<script type='text/javascript' src='http://example.com/wp-includes/js/mediaelement/mediaelement-and-player.min.js'></script>

<script type='text/javascript' src='http://example.com/wp-includes/js/mediaelement/wp-mediaelement.min.js'></script>