There are no Xbox achievements for Original Xbox games because this functionality was not available on the Original Xbox at that time of its release. With system-link (if game supports the feature), you can play with others across Original Xbox, Xbox 360, Xbox One, Xbox One S, Xbox One X, Xbox Series X and Xbox Series S consoles.
However, offline multiplayer scenarios such as co-op, party scenarios (multiple controller on one console), and system-link are supported if they were supported on the Original Xbox. Since these are the original games, not remasters, Xbox Live services such as online multiplayer and in-game marketplaces that were available on the Original Xbox, will not be available.
You can play the digital or disc-based game you own, taking advantage of Xbox features like Game DVR and broadcasting.
