Usually the site's embed code for a video would have the title listed with it, but this mod is made for ease of use. Copy the url in your browser and post it, most users wouldn't care to look at the site for the original embed code, plus it would be a security risk to allow html to be posted directly in the forums.
You just want to ask users to post the title of the video as the post title or put it in the post.
If your modification does put the post title in the post it won't matter. Everytime a video embed bbcode is loaded, which is everytime you load a post with a video. It's all dynamic, it doesn't store the code into the post.
The actual post content contains http://myforum.com/video.php?link=http: ... =videocode
The php file is executed and returns the result every refresh, it's dynamic. The actual embed code is not stored in the post. That is why it's not working.
Also your way will significantly increase load time for any topic/post that has a video and will increase your bandwidth since you are loading someone else's site on your server. So I would just find a mod that actually puts the embed code in the post, unlikely, or just put the the users put the video title in the post themselves.