This isn’t really a Duke3D port/remake, but this project is focused on experimenting with Duke3D resources to provide better graphics/functionality. The last version available gives you the only possibility to fly through opengl-rendered levels and see some engine-related information.
However, it seems that this one will never be finished. If you are still interested, then you can try the following:
Download and unpack release version of game.exe from lduke3d.zip to the directory with original game files (c:\games\duke3d\game.exe, for example)
LDuke3D can only be started with command line keys. The first parameter is “GRP” filename (duke3d.grp in our case), and the second is the map name we want to start (for example E1L1.map, where E1 stands for Episode1 and L1 stands for Level1). So you can click “Run” in Start menu, input something like C:\Games\duke\game.exe duke3d.grp E1L1.map and click OK.
Control keys (taken from project's website):
Mouse
look around
ESC
exit
Q, Z
move up/down
W, S
move forward/backward (+LShift moves slowly, +RShift moves only the camera)
A, D
strafe left/right (+RShift moves only the camera)
Space
jump
R
restart position
F1
switch between solid rendered and wire-frame renderer
F2
toggle debugging rendering on/off
F3
toggle no-clip mode
F4
switches the 'movement controllers' (right now it supports 'walk' and 'fly' controllers)