Some cursory Google-ing reveals no specific announcement on the matter from MLB itself, but, as David Pinto discovered ca. 48 hours ago (and the media on the present electronic page illustrates) video embedding is now available through MLB.com.
Here’s what the page for the above video looks like, for example:
As Pinto suggests — and which even more cursory investigation reveals — there doesn’t appear to be an embed option for the most recent videos. While that makes the discovery less than 100% satisfying, this certainly marks a step in the best direction for MLB.