Taken from the R.E.L.I.V.E. project website:

R.E.L.I.V.E. is a fan effort to create a new engine, capable of replacing Digital Dialect's aging PC port for Oddworld's first two cult-classic games.

More than twenty years after their release, both games struggle to run on modern platforms, usually requiring a third-party application like DxWnd just to run them properly.

R.E.L.I.V.E. intends to become a complete replacement of both the original AbeWin.exe and Exoddus.exe and any third-party tools, by providing both convenience and compatibility features.

Native Resolution Support
It doesn't matter if your monitor is FullHD, 4k or perhaps an old rectangle CRT monitor, R.E.L.I.V.E. supports all.

Windowed mode
No more need for DxWnd or similar, simply press F12 and the game goes into windowed mode or back to fullscreen on the fly.

Modern Platforms
R.E.L.I.V.E. natively supports Windows 10, MacOS and Linux.

Modern Technologies
The re-write uses the modern and cross-platform SDL2 Graphics Library, instead of the long deprecated DirectDraw API.

Open Source
R.E.L.I.V.E. is a fully open-source codebase, which you can freely use for your own projects or extend as you see fit.

Numerous Bugfixes
Tired of the crashes and weird things the game sometimes does? Worry not, the project's scope includes fixing all of these!

Future features
After the engine is fully reimplemented, the focus will shift to adding new features that were never part of the original:

• Subtitles for cutscenes.
  
• Fixing the original games' bugs.
  
• Modding support.
  
• Level editor.
  
• Higher-resolution textures.

You can download R.E.L.I.V.E. over at: https://aliveteam.github.io/.

Windows
These instructions work for both Abe's Oddysee and Abe's Exoddus.

Download the zip that fits your architecture (most likely 64-bits) from the links above.

Unzip it somewhere.

Navigate to where you installed the game (GOG asks you where you want to install it, with Steam you can right click on the game, select Manage -> Browse local files).

Copy relive.exe and SDL2.dll to the respective game's folder from the unzipped folder.

Run the game by launching relive.exe.