SharePoint Classic Video Player taken directly off backend SharePoint Classic, so it just works.
Add this to a script editor web part
Here is the code:
The yellow is the link location to the video
The pink in the link location to the preview image of the video
<div class="mediaPlayerContainer"><video class="mediaPlayerVideoObject" id="FilePreviewID-1-MediaPlayer" onloadstart="" poster="/_layouts/15/images/videopreview.png" width="350px" height="197px" data-init="1" controls=""><source src=https://mysite.sharepoint.com/SiteAssets/video.mp4 data-label="undefined" type="video/mp4"><a href="javascript:Silverlight.getSilverlight("2.0");" style="text-decoration: none;"><img src=http://go2.microsoft.com/fwlink/?LinkID=108181 alt="Get Microsoft Silverlight" style="border-style: none" data-themekey="#"></a></video><div class="mediaPlayerFullScreenEsc"><span></span></div><div class="mediaPlayerInitialPlayButton" style="display: none;"><a href="javascript:;" title="Play"><span></span></a></div><img src="/_layouts/15/images/hig_progcircle_loading24.gif" class="mediaPlayerLoadingIndicator" title="Buffering... Please wait" alt="Buffering... Please wait" data-themekey="#" style="display: none;"></div>
