Результат

Исходники

HTML

<div class="video-box" id="video-box">
<iframe id="video-box" src="https://www.youtube.com/embed/RD6FXWOtijc?enablejsapi=1&mode=opaque&wmode=transparent&autoplay=1&loop=0&controls=0&modestbranding=1&rel=0&autohide=1&showinfo=0&color=white&iv_load_policy=3&theme=light&wmode=transparent&mute=0&playlist=RD6FXWOtijc" frameborder="0" allow="autoplay"></iframe>

<div class="video-content">
<a href="javascript: void(0);" id="play_video">Запустить видео</a> <br>
<a href="javascript: void(0);" id="pause_video">Остановить видео</a>
</div>
</div>

CSS

.video-box {
border-radius: 10px;
position: relative;
overflow: hidden;
}
.video-box iframe {
border-radius: 10px;
position: absolute;
top: 0px;
left: 0;
width: 0;
height: 0;
z-index: -1;
}
.video-content {
border-radius: 10px;
position: relative;
backgrund: background: linear-gradient(0deg, rgba(0,0,0,1) 0%, rgba(0,0,0,0) 25%, rgba(0,0,0,0) 75%, rgba(0,0,0,1) 100%);
padding: 320px;
font-size: 20px;
}
.video-content:before {
z-index: -1;
content: '';
position: absolute;
top: 0px;
left: 0;
width: 100%;
height: 100%;
background: black;
opacity: 0;
}

JS плеера

function setVideoCenter() {
var $box = $('.video-box');
var height = $box.height();
var width = $box.width();
var new_height = width / 1.78;
if (new_height > height) {
$box.find('iframe').css({
width: width,
height: new_height,
top: '-' + (new_height / 2 - height / 2) + 'px',
left: '0',
});
} else {
var new_width = height * 1.78;
$box.find('iframe').css({
width: new_width,
height: height,
top: '0',
left: '-' + (new_width / 2 - width / 2) + 'px'
});
}
}

$(function(){
setVideoCenter();
$(window).resize(setVideoCenter);
});

JS кнопок

<script src="https://www.youtube.com/iframe_api"></script> <!-- Здесь цепляем кода iframe_api-->
<script>

$(document).ready(function() {

var my_video = document.getElementById("video-box");
var my_video = my_video.getElementsByTagName("iframe")[0].contentWindow;

$("#play_video").on("click", function() {

my_video.postMessage('{"event": "command", "func": "playVideo", "args": ""}', "*");

});

$("#pause_video").on("click", function() {

my_video.postMessage('{"event": "command", "func": "pauseVideo", "args": ""}', "*");

});

});

</script>