I cannot comment on the setup this particular store has, but typically if a storefront has a significantly different appearance on mobile compared to desktop, it is because they are either using a highly-modified Shopify theme or a third-party theme. Our themes are designed to be responsive, meaning they have the same components on different devices but adapt to the screen size and device type they are being viewed on. This means for a Shopify-made theme, the mobile and desktop will have the same header image even if they are presented in different ways.
If you're looking to do this for your own store, you would need to hire a Shopify Expert to make this change for you as such a change would be deemed unsupported by our own themes team.
Victor | Shopify Social Care