Interesting.
I got it to work with this simple sketch:

1. import com.citumpe.ctpTools.jWMI;
2.  
3. void setup()
4. {
5.   try
6.   {
7.     String name = jWMI.getWMIValue("Select Name from Win32_ComputerSystem", "Name");
8.     println(name);
9.   }
10.   catch (Exception e)
11.   {
12.     println(e);
13.   }
14.   exit();
15. }

(the page is a bit misleading...)
I made it work by creating a jar file out of the provided archive.
If you want to include the source code in your sketch (as a separate tab), you have to remove the package declaration from this file.

So I'm confused, did you create a JAR file or did you import the JAVA file?  Because I see from your sketch that you imported the jWMI file but you mentioned removing package declarations as well.

I made a jar, but since it is harder for you, I gave the alternative to use the .java file by removing the package declaration, but I haven't tested this solution.
For your convenience, I have put the jar I used in http://filebin.ca/ca9wM0Y1FRN/jWMI.jar (limited availability time).

Thank you very much, it works great.

Redirect output to a file, from the .bat script.