I can't open the settings menu due to my computer being 64 bit.

Have you tried setting it to open/start as Administrator?

Yes. It's not compatable with 64 bit windows. Tsk. tsk. tsk.

I got Win 7 64-bit and have no problem playing that game or the settings menu.

If you can't run setup.exe for Duke Nukem 3D and it gives you that error that the program or feature cannot run due to incompatibility with 64 bit windows versions.
I find that if you have Dosbox installed "http://www.dosbox.com" and run setup.exe if it's for dos in Dosbox 0.74 etc it will work that way.

Here is my Suggestion right click on SETUP.EXE and Select Properties. Once the window pops up click on Compatibility. There should be a selection on the bottom that says Run program as Administrator under privilege level. Then click Apply, problem should be solved.

I also have Windows 7, same problem with that same error message.

I have tried various compatibility modes and running as administrator. No luck.

I'll try dosbox, I just want to run Setup.exe as the shortcut created on install that runs the GOGwrap file seems OK.

Or try using eDuke32 to play. Far superior than DOSBox to play Duke.

Have you tried to run setup trough the start menu folder that should have been installed alongside the game? You should just right-click that start-menu shortcut and select "run as administrator".