Video shortcode outside WordPress not working with IE and mediaelement’s Flash fallback

I figured out the issue. I’m leaving the answer for future reference.

Turns out IE needs you to include all the HTML tags for the video to load correctly when using flash. This is my working code now:

<?php 
    define('WP_USE_THEMES', false);
    require('../wp-load.php');

    echo '<!doctype html>';
    echo '<html>';
    echo '<head>';
    echo '<meta charset="utf-8">';
    echo '<title></title>';

    echo '<link rel="stylesheet" type="text/css" href="https://wordpress.stackexchange.com/questions/198578/wp-includes/js/mediaelement/mediaelementplayer.min.css" />';
    echo '<link rel="stylesheet" type="text/css" href="http://wordpress.stackexchange.com/wp-includes/js/mediaelement/wp-mediaelement.css" />';
    echo '<link rel="stylesheet" type="text/css" href="sample.css" />';

    echo '<script src="../wp-includes/js/jquery/jquery.js"></script>';
    echo '<script src="../wp-includes/js/mediaelement/mediaelement-and-player.min.js"></script>';
    echo '<script src="../wp-includes/js/mediaelement/wp-mediaelement.js"></script>';
    echo '</head>';

    echo '<body>';
    echo do_shortcode('');
    echo '</body>';
    echo '</html>';
?>

Not sure if this is the best way to add HTML to a PHP, but it’s working.