I played this demo when it first came out, it came on a CD with a PC magazine, PC Format I think. It was probably the first RPG I ever played, and I immediately fell in love with Fallout's world. It doesn't look great because it's running in crisp 640 x 480 resolution, but I'm impressed it still runs at all on modern PCs. I wish it had music, I played it twice to explore some of the other things I missed the first time.
You can follow the below steps to play it yourself:
⁍ First download the demo from the Internet Archive. It's just 20mb, so you'll have it in seconds. https://archive.org/details/FalloutDemo
⁍ Extract the contents of the zip archive to anywhere (even just your desktop). You'll be left with a folder called 'falldemo'.
⁍ Inside the falldemo folder you'll find a Falldemo.exe, but don't click it straight away. First, we need to sort compatibility. So, right click on the Falldemo.exe and go to the Compatibility tab. Within that tab, under the Compatibility mode section, select the option to run the .exe in Windows 95 mode.
⁍ Finally, in the same Compatibility tab under the 'Display settings' section, tick the boxes to run the .exe in 256 colours and 640 x 480 screen resolution. You're now set to double click the Falldemo.exe and play the Fallout demo.