I have found the solution and mentioning the same here so that it can be helpful to someone. BUT STILL I WANT TO KNOW WHY DIRECT VIDEO LINK HAS STOPPED WORKING.
The Solution:
In “Modal Popup” direct instead of “Video” in Modal Content Type section. Use “Text Editor” and in code add the embed code of the YouTube Video. This works fine.
But to some video it still might not work and you might get permission error. Solution for this is to login to the Channel of that video on YouTube and from their either give permission (I couldn’t find it though!) or get embed script and use that.