In this case it isn’t the game producer who wanted a piece of the game taken out.
GTA uses real music (that is, regular popular music that is made by stars) in their ingame-radio. 2001 or 2004 respectively the game producer (Rockstar - no pun intended) could acquire the licenses at a reasonable price - mostly because the music industry thought that there is no games “industry” and it’s all a dud for nerds or something. At least something that isn’t near as popular as music.
Ten years later, being hit by MP3 and the Internet revolution in the meantime, the music industry is desperately seeking for new revenue - and found out that licenses still work in their favour (mostly because they did write the according laws).
So they do what big corps do - they blackmail. In this case: dish out a proper cut from your hugely successful games. Computer gaming industry says no. Judges judge that although a customer bought something, they still have no control over it when it’s only been licensed by someone else who then sold it on.