Video cannot be embedded like you would on a website, because it will not work in most email clients and will get stripped out, however, instead what you can do is upload a gif of the video or a still frame of the video and put a red YouTube play button overlay on top of it, and then link that image to the video or to a webpage that has the embedded video.
- Go to the share options and select embed
- Grab the URL portion of the embed code only and paste it into a new tab. your video will be the only thing on the page
- Use CTRL + to zoom in on the video, which also makes the red YouTube play button larger
- Screenshot that and use it as your image