I know it's been awhile since I made the post that you replied to, but I wanted to say thank you. Getting the version of Java you specified was kind of a pain but after getting that taken care of the game now works. Almost two years of issues due to Java. I am genuinely surprised this hasn't been corrected by the developers yet.
Yeah the jre that comes with all versions of the game is the Windows version which is why you have replace it for your OS (I found that out later lol based on the files ending will .dll and .exe). Also I don't think that version is necessary, it's just the first one that worked for me, so I'm sure newer versions work the same?