This is an accepted solution.
Thank you for your message and for providing your store link, I would be happy to offer you some suggestions for this issue.
First, I would like to mention how lovely your live shop looks, I love the clean and professional look and easy-to-use menu system you set up. However, I can see exactly what you mean about your video not playing, have you noticed this issue across all devices, including mobile?
I would first suggest popping into your admin and heading to Online store>Themes>Theme Library and adding a Fresh Shopify theme and previewing it, does your video play as intended on the unpublished Shopify theme? If so, this could point towards an issue with your Grid themes code:
Since the Grid theme is a third-party theme supported by a development team called Pixel Union, I would suggest reaching out to their support directly to look into this issue with you. While it may not be possible within your theme to auto-play your video, it certainly should at least be clickable of course. You can reach out to Pixel Unions support in a couple of ways, first by heading to our official Grid theme page here and clicking "Support and Documentation:"
I checked out Pixel Unions support page for their Grid theme here, and it looks like they have had previous issues with their videos when reviewing their "release notes" over the years, so it may be a current and known glitch with this theme.
Alternately you could reach out to us via our Help Center and log in to create a support request to chat with one of our support members via live chat, email or callback. Once you do so and explain your theme issue, the team member will be able to create a support request ticket on your behalf and send it to your Themes developer.
I hope this information helps you out moving forward, feel free to reach back out here if you have any questions at all!