Well, the game itself was released for old Mac OS versions. Now the great GOG version is playable only on Snow Leopard.
The problem I have now is this: I have a MacBook Pro that still runs under "Tiger". I would like to play the GOG version on this MacBook Pro but can´t because the application is made to run only under "Snow Leopard".

Anyway, when you open ('show package contents') the .app file in the finder, you can navigate to Contents/Resources/game/ and find an older version of the Geneforge.app that runs on older Macs. Now the problem with this is, that this older version is still "unregistered" and therefore only usable as a Demo with severe content restriction. That runs fine though.

Now I want to know if I can get the key to register the game, or if there is another way of how I can run the GOG version on older Mac OS systems.

Avarchillion

HA! Just found out how to do it!

In Finder go to your Library/Preferences and look for a file called "Geneforge Prefs".
Now open a new window and go to your Geneforge 1 (or what ever number).app, right click it and choose "show package contents". Now through go Contents/Resources/ till you find a file called "prefs". Create a double of that "prefs" file. Rename that copy to "Geneforge Prefs" and put this new "Geneforge Prefs" file, into your Library/Preferences folder, replacing the old one.

Now the game is registered and you can play it on an older mac. You of course will always have to use the Geneforge.app that is found within the GOG version of the .app. Just follow the Contents/Resources/game/ path through the GOG app to find the old Geneforge app that runs on the older Mac OS systems.

I just discovered this method on my own, and though some investigation I discovered the same trick you did. It works!