My Java stuff are actually in System32 instead of System32/SysWOW64
That usually means that it is 64bit Java. SySWOW64 is Windows compatibility layer that allows 32bit applications work on 64bit windows. So everything inside that folder is usually 32bit, but outside of it is usually 64bit. You can check which Java you have by opening a terminal (cmd) and typing "java -version" (also post it here). I have "mixed mode" which means I have both 32bit and 64bit.
The error you are having though is slightly different from the one you linked in the troubleshooting page. The one in wiki talks about wrong version of Java. Your error talks about no Java at all. This is usually when 64bit Java is installed (which on modern PC's is the default option), while LGM and ENIGMA right now only works with 32bit Java. Another problem could be the version of Java. At least since version 1.8.0 Java doesn't actually install in system folders. They install in program files, like "C:\Program Files (x86)\Java\jre1.8.0_45\bin". If you have it in windows folder that means you have an old version.
What I suggest you do is download a new version of Java here:
http://www.oracle.com/technetwork/java/javase/downloads/jre8-downloads-2133155.htmlWhen you install it then you should have the problem described in the wiki page, as that is sadly a known problem with new Java and old Java:
http://stackoverflow.com/questions/9313353/error-when-checking-java-version-could-not-find-java-dll ,
http://stackoverflow.com/questions/19329047/could-not-find-java-se-runtime-environment-after-installing-java ,
http://stackoverflow.com/questions/6362037/java-error-opening-registry-key . But people usually don't need old Java and on new PC's with new installations this is not a problem.