Is it possible to tweak/add new domain name to get embedded player work for that. 
Can you fix the embedded YouTube video funtion to also accept youtu.be links
Please, NOOOOO!!!!!!

The youtu.be URLs are helpfully designed to avoid the horrible auto-embedding feature present in so many forums. They are share links, not embed links.
If you want the forum to automatically re-write your link as an embedded video, use the full URL, or use an embed link directly.
If you want the forum to leave your link unmolested, use the YouTube provided share link.
Did you notice that with a full YouTube URL you cannot stop the forum software messing with it? To see how this is bad, try posting a YouTube link with a start time code included. You will notice that the attempt to re-write the link breaks things.
So please, let's leave well alone and not try to break things that are working as designed.