After you've downloaded the .zip file, open it and try to find the executable. This is not yet the logo of the game but instead the standard ren'py logo of a redheaded girl with a yellow snake. When you click on it, the computer will ask you in which map to unpack the .zip file. Let it unzip and once it's done the .zip file can be thrown away. In the new open game folder, click the same option as before (which has now changed it's logo) to start the game. Depending on your computer, starting the game may take a while but it's smooth and lag-free sailing from there on out. Pretty much always will your computer first ask you if you're sure, because it cannot determine if the file is safe (it is).
This technique should work for starting all Ren'py games.