That sounds more like Unreal Championship 2 which was exclusive to the original Xbox, but a cancelled PC port build was
leaked. The first Unreal Championship was very similar to Unreal Tournament 2003 for the PC, but had certain changes made to run on the original Xbox.
The original release should work fine, but you will have to
edit the ini file to use an alternative master server if you wish to play online as Epic shut down the original server, alternatively you can just enter the server's IP address within the server browser. You can also use the
DirectX11 renderer which might help for newer graphics cards, and a Vulkan renderer is in development.