@jebernier : Video headers are considered decorative elements — like header images, but with motion. With that in mind, they play automatically, loop by default, and don’t have sound. They work best when paired with an image, so they can progressively enhance the experience when video is supported.
To alleviate concerns about bandwidth, videos are only loaded on the front page for viewports that are at least 900 pixels wide and 500 pixels tall. The maximum file size is also capped at 8MB; however, we strongly encourage smaller files be used whenever possible. This clearly implies that you can not display videos on mobile devices. The feature is controlled by WordPress core and themes have got nothing to do with this issue. Please follow this link from WordPress core to know more about the issue.