for Linux, last time I checked when you visit the Oracle page and download the jre manually, its just an archive which you extract and then there is a makefile or whatever which "installs" it
you then have the jre at the location you specified, and just like with windows its just a folder which you can just package with the game - using a .sh file to call it or something more sophisticated
so Im sure mac would be similar, just with the App Builder things afterwards
For windows btw I do the same as explained for linux, copy jre folder, make sure you have the server jvm, have .bat file which starts everything, then grab a bat to exe converter which also hides the console, has icons and everything and you're good to go
and then most people use NullSoft Install Script to make installers for windows...
on linux well, not sure what is best... well the BEST way would be to have installers for many different distros
and mac should be done with the aforementioned APPBuilder or whatever its called