I should have mentioned that I do install the official 188.8.131.52 patch beforehand and run UAP091225.exe with admin rights, but that apparently makes no difference.
That is odd :/. I am running the same retail version (when Sierra still had it, gotta find my great manual if I haven't lost it) and doing the 1.074 -> UAP [latest] worked fine for me. I don't install to Program Files by habit (I have it installed in C:\Old Games\Arcanum), have you tried installing to a different location?
Also - do you have a non-US version of Windows by any chance? (with your location as US I doubt it but troubleshooting requires some pretty crazy sounding questions :p)
Do you have any extra language packs installed? Can you post a screenshot of the exact error that comes up when you try to install the latest UAP?
My standard troubleshooting for something like this is to cleanly uninstall the game/app (making sure all registry entries are gone) and then trying fresh [installing games outside of Program Files helps alot in many cases]. If you are using a 32 bit version of windows you can try Revo Uninstaller (it doesn't support 64 bit windows for some reason, and I haven't installed to see if it works properly on my new Win 7 x64 copy yet) - it will search for leftover registry entries and file detritus for you (and its free :D).
Actually, I install all of my games in a "C:\Games\*game name*\" folder out of habit, and have done so since the Win9x days-well before Vista's UAC became a possible issue with anything installed to Program Files.
Yes, I run US copies of Windows, with no extra language packs (given that I'm only monolingual and all, as much as I hate to admit it). That UAP spits out the same error on Windows Vista 32-bit and Windows 7 64-bit (though I just replaced the former case of Vista with Windows 7 64-bit as well, but have yet to re-install Arcanum on this system).
You had to bring up the manual, though. I want to slap whoever put this boxed copy of Arcanum in a thrift store with a manual that has several holes poked through it, tears on the cover, the last two pages cut in half, and pretty much ruined. Still sort of readable save for the last two pages (which apparently aren't that important), but now I'm wishing for the Microsoft Courier to become reality already so I can read electronic manuals on it in addition to taking notes and sketching.