What was the name of the Xbox 360's online digital marketplace for downloadable games?

The Xbox 360’s online digital marketplace for downloadable games was called Xbox Live Arcade.

Xbox Live Arcade, commonly abbreviated XBLA, distributed downloadable games through Xbox Live. The service became especially important on Xbox 360, where players could buy smaller independent productions, arcade revivals, experimental games, and digital versions of classic titles. Games were downloaded to the console and linked to a player’s Xbox account.

Xbox Live Arcade is sometimes confused with Xbox Live Marketplace, the broader digital storefront that also covered downloadable content, themes, videos, and other items. It is also distinct from Xbox Game Pass, a subscription service that launched much later.

Notable Xbox Live Arcade releases included Geometry Wars, Braid, Limbo, and Castle Crashers. The service helped establish downloadable games as a major part of console distribution before digital-only libraries became standard.