Hack the default WordPress video player if you want a width different than the $content_width global.

functions.php

/**
 * This function is the same as str_replace but once
 * A small warning: this has not been tested in RSS feeds.
 * Thx @ScreenFeedFr for the hack
 * @link    https://twitter.com/ScreenFeedFr/status/492056927745343489
 * @param   string   $search   Value being searched for.
 * @param   string   $replace  Replacement value
 * @param   string   $subject  String being searched and replaced
 * @param   boolean  $rev      I don't fucking know what this var do :)
 * @return  string             Replaced value
 */
if ( !function_exists('pp_str_replace_once') ):
function pp_str_replace_once( $search, $replace, $subject, $rev = false ) {
    if ( ! $rev ) {
        if ( false !== ( $pos = strpos( $subject, $search ) ) ) {
            return substr_replace( $subject, $replace, $pos, strlen( $search ) );
        }
    } else {
        if ( false !== ( $pos = strpos( strrev( $subject ), strrev( $search ) ) ) ) {
            return strrev( substr_replace( strrev( $subject ), strrev( $replace ), $pos, strlen( $search ) ) );
        }
    }
    return $subject;
}
endif;

/**
 * This is where the magic takes place. Lets build a responsive video player.
 * @param   string  $html     Our html code for the player
 * @param   string  $atts     height, width attributs
 * @param   string  $video    video url
 * @param   string  $post_id  the post ID
 * @param   dunno?  $library  Don't know what this var do
 * @return  string            Return the html code for the video player with modified values
 */
add_filter( 'wp_video_shortcode', 'pp_responsive_video_hosted', 10, 5 );
if ( !function_exists('pp_responsive_video_hosted') ):
function pp_responsive_video_hosted( $html, $atts, $video, $post_id, $library ) {
    if ( !empty($atts['width']) && !empty($atts['height']) && preg_match( '@ style="width: (\d+)px; max-width: 100%;"@', $html, $matches ) ) {
        $width   = (int) $atts['width'];
        $height  = (int) $atts['height'];
        $padding = round($height * 100 / $width, 2);
        // Change padding for non 16/9 videos. Allow 0.02% tolerance.
        $replace = abs($padding - 56.21) > .02 ? ' style="padding-bottom:' . $padding . '%"' : '';
        $html    = pp_str_replace_once( $matches[0], $replace, $html );
    }
    return $html;
}
endif;

style.css

.wp-video {
    position: relative;
    width: 100% !important;
    max-width: 100%;
    height: 0;
    padding-bottom: 56.21%;
    margin-bottom: 1.5em;
    clear: both;
}

.wp-video > div,
.wp-video > video {
    position: absolute;
    left: 0;
    right: 0;
    top: 0;
    bottom: 0;
    width: 100% !important;
    height: 100% !important;
    margin: 0;
}

.mejs-layer,
.wp-video-shortcode { 
    width: 100% !important; 
    height: 100% !important;
}