Hi Dana and thanks for the rating/review ;)
If you want to code this directly into your theme you would just have to replace the line
'terms' => 'echo get_post_meta($post->ID, 'release_date', true) ',
with
'terms' => get_post_meta($post->ID, 'release_date', true),
and it should work.
But I've also added a new filter option "+postMeta:key" to the shortcode (v1.6.7).
So in your case you could use
[relatedYouTubeVideos relation="postTitle" max="2" width="350" filter="official video +postMeta:release_date " duration="short" height="170"]
without having to hack any code.