I'm not sure the embed shortcode accepts a shortcode as a parameter so this is why its possibly not working.
What I recommend that you do is to recreate this field in Types so you can use our methods of displaying the embedded media.
If the embed shortcodes that wordpress provides accepts shortcodes then it should work fine but since its not working its only fair to assume that it doesn't.
If there isn't alot of posts that are using this field then you should be able to just quickly re-create this in Types and use the embedded media field and just re-add your links to the posts.
Then you can just display the items without the use of the embed shortcode.
Please let me know if this is clear or if you want me to explain this a little further for you.