Before online gaming, the original Xbox depended on system-link. System-link is multiplayer gaming on the same network. The original Xbox, Xbox 360 and Xbox One are all compatible with system link even though it started in 2001 on Xbox.
The original Xbox is the first generation Xbox, the Xbox 360 is the second generation and the Xbox One is the third generation. As long as the Xbox game is backwards compatible i.e. Crimson Skies and system-link compatible then the game will work across all three platforms. There are over 150 system-link original Xbox games. To play system-link across two different Xbox, all you'll need is either a system-link cable (cross over cable) or an Ethernet cable (internet cable) and a router)
You may also want to know, system-link original Xbox games can still be played online today for free via X-Link Kai. X-Link Kai is a program that tricks the Xbox into thinking the online multiplayer connection is a system-link connection allowing you to play online. If you softmod your original Xbox you can run the Xbox game straight from the hard drive to play. Even some homebrew Xbox games and ports added a system-link feature i.e. Doom-X, Quake, Quake 2 and Duke Nukem 3D and many more.
It's important to note, that when running system-link games they have to be exactly the same i.e. a greatest hits/classics version is not system-link compatible with an original black label release of the game.
source: https://www.youtube.com/watch?v=r0j9LEHwsCo
