You don't need to install OpenJDK to run the portable version and the installer versions provided at download page, because they come with their own copy of Oracle Java.
I don't see any change in the program between versions 4.4 and 4.6 that could make it fail on your computer. Did you try the version 4.4 available at https://sourceforge.net/projects/sweeth ... ome3D-4.4/ ?