Does <?php the_title(); ?> echo something if you put it after your if clause? The WordPress codex about The Loop as example states the following:
<?php if (have_posts()) : ?>
<?php while (have_posts()) : the_post(); ?>
<!-- do stuff ... -->
<?php endwhile; ?>
<?php endif; ?>
the_post() calls $wp_query->the_post() which advances the loop counter and sets up the global $post variable as well as all of the global post data.
The plugin requires the global post data to be set in order to determine which video is requested.
Alternatively you can use has_post_video($post_id), where $post_id is the ID of the post from which you want to pull the featured video. This could be of interest for a front page, where only a single specific post or page is displayed all the time. You can determine the post ID on the post's edit screen from the URL: [...]/wp-admin/post.php?post=42&action=edit, 42 being the post's unique ID.
Hope this solves your problem! Alex