The Windows version without Java is for users who can take care of installing a JDK (not JRE) themselves. It should only be downloaded by advanced users who are familiar with Java.I opted to download Processing without the JDK, so that I could learn how to set up my environment manually.
Installing the JDK
http://docs.oracle.com/javase/7/docs/webnotes/install/windows/jdk-installation-windows.html
Components in green, I installed, those in red, I did not.
- Development Tools
- Demos
- Source Code
- Public Java Runtime Environment
Installing Processing
http://processing.org/download/
The Processing installation was straightforward; extract the archive, move the folder to a permanent location, then run processing.exe from a shortcut for convenience.
The Outcome
A working Processing environment for me to start playing in, shown here running a Words example on my PC desktop.

Click image to enlarge