A while ago I was playing around with a programme called
Executor, which is a now discontinued compatibility layer project to run Mac 68k applications on IBM PC compatible hardware. This programme has its drawbacks and not all Mac emulation features are supported, but unlike the vast majority of Mac emulators it does not require anything from Apple: no authentic Mac ROM image, no copy of MacOS etc, are needed to run Mac software.
I have found two different Mac 68k demo versions of
Duke Nukem 3D:
duke3d.sit.hqx and
duke68kdemo.bin. Both run in Executor, however with some limitations.
I will not be describing the basic procedures of setting up Executor. Those can be found
here.
Duke Nukem 3D demo versions will not run if you just double-click the executable file. This may or may not have something to do with logos and intro animations shown at startup. To get the game running you need to use Cmd-click (hold Alt and double-click the executable) to bring up the startup options menu:

This is basically the equivalent of DOS command line options. From here, you can warp to any of the three demo levels. It seems that there was a Mac convention that a demo should have three levels. This holds true for other games such as
Doom,
Descent etc.
Wolfenstein 3-D kind of circumvented that by making a shorter version of the shareware episode: you don't get the first three levels, you get level one, some intermediate level, and the boss battle. In
Duke3D however, it's just E1L1 to E1L3.
When you warp to level 1, the game looks like this (it seems to always load default settings, although I'm not sure if this is because of some Executor limitations or a feature of the demo):

As many other Mac ports of DOS games,
Duke3D runs by default in 640x400 mode vertically centred on a 640x480 screen. Additionally, it is capable of using scanlines to increase performance on slower machines. Scanlines can be turned off, and the game can also run in the usual 640x480 mode as well, which is identical to the DOS one. Additionally you can select 320x200 which will be centred on the 640x480 screen. Here's the graphics settings menu:

BTW, most control keys work as you'd expect on the DOS version. The menus however use Mac windows rather than menu lists drawn by the game itself, with the exception of the main menu:

The game uses the Atomic Edition font, but does not call itself Atomic Edition, because the Mac port already included all four episodes, having been released later than the vanilla DOS version.
Unlike the DOS shareware version, the Mac demo includes player AI in fake multiplayer mode, and you can set up a game with up to 8 players:
BTW, the Mac demo GRP file can be opened with Group File Studio, and I guess other tools as well. Executor will not run the cheat code-activated Mac 1984 commercial in E1L1 because there is no Quicktime support, but the other Mac cheat that changes the security cameras background will work fine.
If you want to try this out yourself, here's how to start the demo in Executor: Alt+double-click on the demo executable to bring up startup settings. Then press Shift+Alt+5 to open the Executor preferences menu for running the demo. Change Screen Updates to Animation, set Refresh to 5 and System to 7.0.0. Sound should be Pretend, and you can also select Newline Mapping (although I'm not sure if this affects anything). Click Save. The preferences menu will stay but you can just click the visible OK button on the demo options to start the demo. Next time you start it just Alt+double-click the executable and run the demo with the options you like.