Hi,
For the exact question regarding Unreal Tournament 2004 in your post see @leileilol's post, for the more generic question made in the title of this topic I can add this:
Unfortunately I don't think there is a compiled list of those available on GitHub, there are online lists available that lists open sourced software in general, but they didn't filter it for GitHub and none of them are close to be an exhaustive list.
One thing is that if a company open sourced one of their games it is likely they have open sourced others, so if you find an open sourced game on GitHub for example:https://github.com/id-Software/Quake-III-Arena it is worth to check out https://github.com/id-Software.
Also a comment regarding your post, while the Command and Conquer: Generals and Quake III Arena source code releases contains both the Game Logic and the Engine and both of them use a GPL license, the Half-Life Source release only contains the Game Logic and Client DLLs and not the full engine, also the Half-Life Source uses it's own proprietary license and not one of the common ones. Of course you mention modding in your opening post, so this is most likely not a concern if you only intend to do a mod for HL and not upgrading the engine itself, the Game Logic and Client DLLs for GoldSrc gives quite a lot of control over the engine's features even without having the full engine source available.
"A process cannot be understood by stopping it. Understanding must move with the flow of the process, must join it and flow with it." - Dune
