Shopify product cards show a still frame even when the first media item is a video.
By default Dawn and Horizon render a product card with the featured media's preview image, so a video in position one appears as a still.
A short edit to card-product.liquid makes the card render a muted, looping, inline video when the featured media is a video.
Play only the cards on screen, use preload none and a poster, and cap how many cards carry video, or the collection page will get slow.
If the goal is video that sells rather than cards that move, a shoppable widget on the collection page is less code and easier to measure.
Yes, with a theme edit. Dawn and most Online Store 2.0 themes render the featured media's preview image on cards.
The full guide has the formats, the deadlines and the worked examples.