The original code ‘should’ be responsive… but i assume the source code didn’t provide that.
You can try adding this CSS:
.mejs-container, .mejs-overlay.load {
width: 100% !important;
height: 100% !important;
}
.mejs-container {
padding-top: 56.25%;
}
.wp-video, video.wp-video-shortcode {
max-width: 100% !important;
}