JSFiddle - React, Tailwind, and code Playground

HTML

<div class="one"> CONTENT OVER VIDEO
    <video class="video-background" no-controls autoplay src="https://dl.dropboxusercontent.com/u/8974822/cloud-troopers-video.mp4" poster="http://thumb.multicastmedia.com/thumbs/aid/w/h/t1351705158/1571585.jpg"></video>
</div>

<div class="two">
    <video class="video-background" no-controls autoplay src="https://dl.dropboxusercontent.com/u/8974822/cloud-troopers-video.mp4" poster="http://thumb.multicastmedia.com/thumbs/aid/w/h/t1351705158/1571585.jpg"></video> CONTENT OVER VIDEO
</div>

CSS

body {
    overflow: scroll;
    padding:  60px 20px;
}

.one {
    width: 90%;
    height: 30vw;
    overflow: hidden;
    border: 15px solid red;
    margin-bottom: 40px;
    position: relative;
}

.two{
    width: 30%;
    height: 300px;
    overflow: hidden;
    border: 15px solid blue;
    position: relative;
}

.video-background { /* class name used in javascript too */
    width: 100%; /* width needs to be set to 100% */
    height: 100%; /* height needs to be set to 100% */
    position: absolute;
    left: 0;
    top: 0;
    z-index: -1;
}

JavaScript

function scaleToFill() {
    $('video.video-background').each(function(index, videoTag) {
       var $video = $(videoTag),
           videoRatio = videoTag.videoWidth / videoTag.videoHeight,
           tagRatio = $video.width() / $video.height(),
           val;
        
       if (videoRatio < tagRatio) {
           val = tagRatio / videoRatio * 1.02; <!-- size increased by 2% because value is not fine enough and sometimes leaves a couple of white pixels at the edges -->
       } else if (tagRatio < videoRatio) {
           val = videoRatio / tagRatio * 1.02;
       }
       
       $video.css('transform','scale(' + val  + ',' + val + ')');

    });    
}

$(function () {
    scaleToFill();
    
    $('.video-background').on('loadeddata', scaleToFill);
    
    $(window).resize(function() {
        scaleToFill();
    });
});