If you share the url we can take a look and try to debug for you.
First place I would check is the browser console to see if there are any errors.
Thank you for your reply. This is the video that was working on my website https://www.youtube.com/watch?v=fl6xDkpVdU8&feature=youtu.be
Here is my website. Scroll down to find the video link. https://sakuradreamsdollfiedreamshop.com/
It looks like it's embedded in a custom way (rather than a standard embedded Youtube video).
Here are 2 solutions:
A) Embed the video from Youtube and insert the embed code into your theme where you want it to show up. This blog post will help you make sure it sizes responsively: https://speedboostr.com/how-to-embed-responsive-videos.
B) I'm guessing the option to play is not working because of broken code. The console is a good place to start debugging, these errors (in red) should be fixed:
If you're not familiar with the console and fixing errors, this post will help: https://speedboostr.com/finding-and-fixing-server-errors.
If you get stuck and need professional help send me a message. My company (from those links) works on Shopify sites every day.