Wow. I was expecting Processing to be a graphics library that could be used by Java programs. Instead it's an IDE with an in-built interpreter for the Processing language.
I am guessing that in reality the core of Processing has been implemented as set of Java classes and that the 'interpreter' is actually a pre-processor that translates the Processing code into Java code.
If my guess is correct, the approach reminds me of JSP pages which are pre-processed into implementations of the HttpServlet Java class before being compiled and executed.