Hi Franz,
The noJRE package is meant to be platform independent, so it does not include a JRE or the pre-compiled Postgres binaries. That is the reason it's not showing up in the list of supported database backends.
Download the installer package specific to your operating system and that should fix the problem. If you are installing on a platform we don't support right now, we can help you through installing Postgres if you need.
-Ryan