I would think it depends on the app, honestly, but I'm not a dev so I don't know.
Just saying that current games or apps that are on the Galaxy S and S 2 play store should be portable to the S 3. There should be no changing of code in regards to the main menu button. So, you are right to say it's the apps.
In my understanding even apps that do not overtly accommodate a menu button like the Galaxy S family does, do have some form of mapping that fits in perfectly, meaning Samsung has got that figured out.
The thing is ICS was created with onscreen buttons exclusively, as designed by Google. HTC's implementation was to use capacitive buttons to do the same. Samsung however designed the S3's buttons even before ICS was released, so they aren't really at fault. It could have been solved by good manufacturer and Google developer communication.
It most likely requires a little more work on the part of the developers to continue adapting their control schemes to support the S3, and that is a byproduct of Android being open source.
Sent from my HTC One X using Tapatalk 2