Thank you for this hint, @Matteobin007! For anyone else interested in running on Linux:
1. Unzip Nightmare Frames.zip
2. Run agstract to extract the data from Nightmare Frames.exe to a new directory, and then agspack to create a nightmare.ags from that directory (both found in agsutils)
3. Download and extract the AGS runtime (v3.6.2.21 works)
4. Copy the the nightmare.ags (from step #2) and English.tra (from step #1) to the data folder (from step #3)
5. Run ./startgame