Depends on what platform you're playing.
If on Windows — the zip file should contain a folder with an .exe file in it, along with few other folders and engine files. Also make sure that your anti-virus (McAfee especially) is not flagging the zip file as dangerous, because they tend to do that with RenPy games.
If on Android — it's indeed only one .apk file that will let you install the game on your phone.
On Mac it's an .app file and on Linux it's tar.bz2 archive.
Make sure you download the correct version that suits your platform.
