The magic padding number you create for the container needs to match the aspect ratio of the video. If you inspect the video on vimeo, the res is 1296×540. To get the aspect ratio percentage, divide 540 / 1296 * 100% = 41.66666667% padding.
Here’s a fiddle since the video doesn’t seem to play well in the SO sandbox. https://jsfiddle.net/mcoker/p7q6x4d5/1/
.embed-container {
--video--width: 1296;
--video--height: 540;
position: relative;
padding-bottom: calc(var(--video--height) / var(--video--width) * 100%); /* 41.66666667% */
overflow: hidden;
max-width: 100%;
background: black;
}
.embed-container iframe,
.embed-container object,
.embed-container embed {
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
}<div class="embed-container">
<iframe src="https://player.vimeo.com/video/208791851?autoplay=1&loop=1&background=1" frameborder="0" webkitAllowFullScreen mozallowfullscreen allowFullScreen></iframe>
</div>