Debugging it, found it uses
$this->get_image_id( site_url() . $dfiImageFull );
in dynamic-featured-image.php:line 681+685
to read the ID of the image. This will fail since the old database holds the old site_url as part of the wp_posts.guid.
I think the fast and selfmade solution for non-developers is reuploading the images on the new server and relinking them as featured images to the posts of your desire.
I would highly recommend the authors of this plugin to store the ID of the attachment within the serialised custom post meta dfiFeatured or think of something more fail-proof.