There is no nature of discontinued systems, it is simply a fact of something not getting an update. What worked will still work. Newer programs will not start due to the missing command library entries (commonly called mismatched DLLs) and that's all. UT2004 isn't a new game so there is no problem regarding this. If Win7 had problem running UT2004 to start with then simply play it on WinXP as I do. I have a separate old PC with WinXP and Win2000 installed because that machine runs these old games with uncomparably better performance even compared to Win10. But I have to say I had no problems with UT2004 on Win7 though there are some not significant issues when I run it on Win10.

I really recommend using the 64 bit executable. If nothing help you still can set OpenGL as the game's default driver which may has poor performance but will work regardless of PC settings. Also installing DX9 separatelly never hurt lol.

Actually when you take down a domain it will not work anymore.
The Game DLL tried to contact a domain that MS no longer host.
Unlike a web browser or well coded tool it does not timeout.

Yes Windows 7 should have got an update to remove or fix the function, but they didn't.
The same non-running of old games in the list happened if the user was offline during the period the system still worked.

Evidence of not needing missing runtime libs is shown when you try running a second copy of the game and like magic it opens.

As I said previously. this only affects users that can see their games listed in windows own games section.
If not listed then your games has not been added to the list for monitoring.
If the game was never used online during the time the system was in operation, it will not be in the list.

This became a major topic in the UT99 communities when it started happening, leading to several solutions.

The thing to note with the GL and DX renderers is the way they allocate RAM on different chipsets.
For some peculiar reason the GL renderers used with ATI/AMD GFX do not use the RAM on the card, but uses system RAM instead.
Depending on which RAM is faster you may see a hit to performance.
Many years ago Intel had a problem with OpenGL and 2 hardware 3D functions, so swapped them for software.
It seems they still haven't fixed the issue or bothered to swap back.
It has been done with a simple blacklist system so is easy to find out if your intel GFX is still using software 3D.
Get a 3D OpenGL screensaver that is complex and maybe makes the intel laggy.
Now rename the screensaver extension from scr or SCR to use mixed case, eg. sCr, ScR, scR etc.
Run the screensaver again, and if it is a lot faster then you can see immediately.
So far this has worked on every intel GFX I have tried.

General rule of thumb for best performance.
OpenGL for nVidia
DirectX for ATI and Intel

Epic did do one previous early patch with a DX9 renderer but it was unfinished and they never went back to it.
I tried it but it crashed on most systems. The one in the x64 patch works well and is stable.
I can't give an opinion on the GL renderer in 2k4 as I never used it, but I have a feeling that like the DX9 renderers it is complete but beta, like the GL renderer in UT99 was.

Indeed it can't hurt to install the DirectX 9 runtime files anyway if not done already, because MS only included basic support for older DirectX since Win 7 and DX11. Only the missing files will be installed.

Win7 work with fully offline PCs while Win10 somehow loss compatibility and while I haven't experienced it yet my friend suspect performance decrease while not having internet connection. If that is true then Microsoft is stupid for enforcing a kind of online DRM. But since we're talking about old games you can always replace the new DLLs with an old one by placing it next to the .exe to overwrite the command request. For Win7 this worked like magic so you may try placing WinXP's set of DLL in the UT2004's system folder (if I remember right that is where its .exe located). This should work with Win10 but I haven't tried it yet.

I know it's late, but have you have tried this?

http://www.unrealcentral.com/ut2004-unreal-tournament-2004-64-bit-patch/