You should follow EXACTLY the procedure descibed on the website below the ftp and http downloading buttons.
this is probably th readme you mention.
It is important that you NOT UNZIP the archives, but instread copy them in a directory JavaCheck (eg c:\jdk\JavaCheck) and run both commands like
java -cp javacheckinstall.zip JavaCheckInstaller
jre -cp javacheckspecinstall.zip JavaCheckSpecInstaller
(notice that "jre" is changed into "java")
This will install some docs, the PersonalJava 1.1 spec file and the JavaCheck.jar program archive.
You can invoke the graphical version by
java -cp c:\jdk\JavaCheck\bin\JavaCheck.jar JavaCheckV
as described in the docs