single-shorthand_story.php

<?php get_header();

        if ( post_password_required( $post->ID ) ) {
            echo get_the_password_form();
        } else {

        	while ( have_posts() ) : the_post();
        		$meta = get_post_meta($post->ID);
        	?>

        	<?php echo trim($meta['story_body'][0]); ?>

        	<div id="extraHTML">
        		<?php echo trim($meta['extra_html'][0]); ?>
        	</div>

        	<style type="text/css">
        		<?php echo get_option('sh_css'); ?>
        	</style>

        	<?php
        	endwhile;

        }

get_footer(); ?>

Added a post_password_required() check and then output get_the_password_form() if true.