You can use Javascript to dynamically set the height to 100% of the window and then center it using a negative left margin based on the ratio of video width to window width.
var $video = $('video'),
$window = $(window);
$(window).resize(function(){
var height = $window.height();
$video.css('height', height);
var videoWidth = $video.width(),
windowWidth = $window.width(),
marginLeftAdjust = (windowWidth - videoWidth) / 2;
$video.css({
'height': height,
'marginLeft' : marginLeftAdjust
});
}).resize();