I have a site that has a section for a blog. The blog sits inside /blog/. What I am trying to do is include a popular post plugin in my sidebar across the site, inside and outside the /blog/ directory.
You need to include the wp-load.php file in order for this to work. You should then have access to all of wordpress' functions. Doing so will impact your performance, however.
You could also use an RSS feed to pull data into your non WP page.
I don't think that the popular posts plugin has its own rss feed, plus there would be some additional overhead in accessing and parsing the rss feed. That solution would be appropriate for a remote site, but if you have access, including the necessary file is easier and more efficient.
$query = "SELECT * FROM wp_posts ORDER BY comment_count DESC LIMIT 5";
Of course this only determines the popularity based on how many comments the post has. I'm not entirely sure where the plugin you're using gets the stats from to determine the popularity of the post.