After I finished downloading this game through the GOG downloader, clicking "install" opened up a .bin file in VLC media player. After uninstalling VLC media player, clicking "install" again did nothing. so I decided to restart the GOG downloader, but when I did that The Witcher 2 was gone from the download list.

They tell me there should be a standard setup.exe file for this game but I can't find it at all. All that's in the GOG downloads folder is all the CHUNK files.

Look at the attached pic. Those are the files you need to install the game. If you're missing the .exe file you can downloaded it manually with your browser and place it in the gog download folder and then double clikc the .exe to start the install.