The Full screen button hides this site's menus so only the games show, on any device. To also hide the browser's address bar so a child cannot open other websites, set up the device once:
iPhone & iPad
Open the Share menu and choose Add to Home Screen - the site then launches with no address bar. For a full lock, turn on Guided Access (Settings > Accessibility > Guided Access), then triple-click the side button on this screen.
Android
Use the browser menu's Add to Home screen, or turn on Screen pinning (Settings > Security > Screen pinning) and pin this screen.
Computer
Press F11 (Windows) or Control-Command-F (Mac) to fill the screen.
None of these approaches is a substitute for adult supervision, especially for older kids.