Howdy. 16" MBP with an M1 Max chip (and macOS Monterey 12.2.1). DN3D AE via GOG installs, but instaquits without error when I attempt to launch it. Any experiences or ideas?

Likely this is due to the recent MacOS dropping 32-bit compatibility since 10.15.

My earlier reply was quite brief as I had to leave, but I've got time to go into some more detail now.

If you're referring to the Atomic Edition (not the Anniversary Edition), then the reason it won't run is because GOG's installer comes with a standalone version of Boxer which is no longer compatible with MacOS since 10.15 (due to the 32-bit issue). GOG was updating many old DOS installers to use DOSBox instead, but it looks like they never did this one.

You will need to either install DOSBox or Boxer64 to your computer (I personally prefer Boxer64 https://boxer.thec0de.com/), and use that to run the game.

Because the game is already packed within the old Boxer standalone, you will need to get the game folder out of the app. Right-click on the Duke Nukem 3D app and select "Show package contents" then navigate to:
Contents > Resources > Duke Nukem 3D.boxer [right-click and "Show package contents"]> C.harddisk
That last C.harddisk folder is the game itself, that's the part you will need to insert into DOSBox or Boxer64.