If you movies are stored in /wp-content/movies/
and the URLs are site.com/movies/movietitle.mp4
then the links are pointing to the wrong place.
Change the URL’s to include the wp-content
path eg site.com/wp-content/movies/movietitle.mp4
Separate to your question, you could look at having your page-movies.php
template load the links into a video element using javascript.