Right click in the you tube video screen, choose copy embedded code, then come to your blog and right click/paste at the point where you want to embed the video. You can also use the tool ( top third button) and paste the code in the pop up screen.
cheers and good luck
Here is test blog with embedded " target="_self">code
copy paste this code into media link.
<iframe width="475" height="267" src="//www.youtube.com/embed/DbgEB5Cnrww?feature=player_detailpage" frameborder="0" allowfullscreen></iframe>
I assume it is the browser you have. Just post the blog for approval, I will add the video at the point you mark " Video" and get it done. Not to worry. Is the video posted in my test is the same you want in your blog?
Also I noticed the link of you tube us secured https one which might be the trouble.
The code works for me: