I mean it does use the Eduke32 engine. Then again the Wii may not be powerful enough.
Wiibrew: At present, using game modifications is possible with EDuke32 Wii but it requires following of a specific procedure. By default, EDuke32 Wii searches for game data both in the directory in sd:/apps/ where it exists, and sd:/apps/eduke32/. This allows you to make copies of the program to have multiple entries in the Homebrew Channel without requiring you to make extra copies of the game data and waste disk space.
Copy your mod's game data to sd:/apps/eduke32/. Next, make a copy of the eduke32 folder in apps where you can add your mod's information.
Once you have made a separate folder for your mod, open the mod folder's meta.xml. Edit the name field to contain something different so you can distinguish it in the Homebrew Channel. At the bottom of the file, you should see the following: