Works for me. You're clicking the big icon that matches your operating system?

I think so.....Hold on i shall check :)

Get the HRP which includes EDuke32.

When i download eduke it says i need to purchase a copy from gog but i have already bought the game. Can anyone help me out? :(

So presuming you're using windows.

You run the GOG installer
You click this link: http://dukeworld.duke4.net/eduke32/synthesis/eduke32_latest.zip
You unzip the download into the folder where the GOG installer put the original game. (Something like C:\Program Files\Gog.com\Duke Nukem 3D, but that might depend on your computer and my fuzzy memory.)
You double click on the resulting eduke32.exe

If you want you make a shortcut to eduke32.exe