MagicDuel keeps you logged in with a single cookie, and your browser is refusing it. Nothing here can remember you from one click to the next, so the game cannot run.
Chrome, Edge, Brave. Click the icon at the left of the address bar, then allow cookies for magicduel.com. In Settings, look under Privacy and security, Third-party cookies.
Firefox. Click the shield at the left of the address bar and switch protection off for this site, or add magicduel.com under Settings, Privacy and Security, Cookies, Manage Exceptions.
Safari. Settings, Privacy, and clear "Block all cookies". On iPhone the same switch is under Settings, Safari.
A private or incognito window also blocks what the game needs on some browsers. An ordinary window works.