Because digital purchasing is dead for Xbox 360, your only way to get a playable disc is:

For the authentic, unmodded experience with modern gameplay features, you can find the game for supported platforms at retailers like or through an subscription. or perhaps a list of officially supported sports games for that console? FIFA 21 but it's on Xbox 360

A closer look at EA Sports’ release history confirms this impossibility. The last FIFA title released for the Xbox 360 was FIFA 19 , which arrived in September 2018 as a “legacy edition.” That version offered only updated kits and rosters, with no new gameplay features or game modes. By 2020, when FIFA 21 launched, EA had officially ended support for the Xbox 360 and PlayStation 3. The company’s business model relies on pushing technological boundaries to justify a full-price annual purchase. Developing and maintaining a separate, downgraded version for obsolete hardware would be economically inefficient. Therefore, when a user searches the Xbox 360 Dashboard for “FIFA 21 Download,” the search yields no results—not because of a glitch, but because the product was never created for that ecosystem.