In autoresponders and broadcasts and emails in general, we don't recommend embedding videos directly into the email. Although some email systems will allow it to work (gmail for example), many will not.
In fact, most email programs on computers (and phones even) won't display embedded videos in emails at all. It will show up as an empty box.
So, the next best thing is to take a screenshot of the video, and embed that into the email template. Then link that image to the video online, either youtube or your own webpage where you have the video embedded.
Here's a quick demo of what I'm talking about (notice when you click the image of the video, it will open up the webpage)
This way, people will go to click on what they think is the play button, and it's actually a hyperlink to the video online which of course opens the web page so they can view it in the browser.
By the way, the whole image is linked to the video online, not just the play button.