Is the nw_elf.dll file in the same folder as Game.exe you're running? If it isn't, it means either your download has been corrupted or there's something removing it from the directory after you extract the game, usually an antivirus. Do you run any antivirus and, if you disable it, re-download, extract and run the game, do you get the same error?
Can you try using the itch.io app to download the game as leafo suggested below?
So, does it work now?
You needed to extract it as that's how archive files work, if that was the question. They are just files and when you run Game.exe from directly from the archive it actually just extracts to a temporary folder on your computer in the background without extracting everything else and then runs, but as none of the other files around it have been extracted it just crashes immediately.