The launchers have absolutely nothing to do with the game, it's simply a script to execute the code through the JRE. There are different launchers for Mac and PC, because the method of telling the JRE to execute code is different depending on the syntax of the operating system.
Additionally, one does not even need to use the launchers to run the game.
That's a difference with each machine's version of Java, not the game. The game itself is identical. This is as explicitly as code can be cross platform as possible, this isn't a technicality or a "gotcha" like you're implying. This is how cross-platform code works.
EDIT: Further, if we're talking technicalities, claiming these are two different versions of the game because their launchers are different is much more of a technicality than claiming they're the same code. This is how virtual machines work. Are you familiar with the concept of an emulator? If I take a Sega Genesis cartridge, dump it, and run it on a PC through an emulator, is that a different version of the game than the one running on my actual Sega Genesis? This is an identical concept.
