Games on iPhones and iPads are primarily designed with touch controls in mind while some do have support for the few game controllers that are compatible with Apple’s mobile platforms. That’s true for “normal” apps but even truer for games. Even when they do, however, not all apps may work perfectly on a desktop or laptop context, at least not without some adjustment. Developers have to indicate that they want their apps to run on macOS on these M1-powered Macs. Support for running iOS and iPadOS apps isn’t automatic nor perfect.
