I don't want to see video ever embedding in this forum for many reasons (few of them are privacy and security), and I don't see why posting link and screenshot is not enough.
Videos in forum will mostly make trolls and spammers happy and maybe even slow forum down.
Actually no, the videos are hotlinked from YouTube so they do not utilized lots of bandwidth except for the image preview and embedment, which is pretty negligible.
Both the youtube player and the video content is streamed from Youtube's server. The only price you pay is the few bytes it takes to add the video player embed code in your HTML pages.
Source:
Bandwidth Data implications of embedding Youtube videos in my website