I do not know about music ai generators. But running something like stable diffusion on your local machine does not require any more energy than running a game does.
And it would calculate an image every few seconds. Rendering complex images in a ray tracer would take hundreds of times more time than that. So any energy argument would hit ray tracing and playing games as well. Playing games even harder.
Where the energy consumption really is a huge isssue, is crypto currency. That is literally bragging how much energy you wasted to calculate an inane math problem.
For something like developing a game or a game's music, the driving factors for decisions would include how potential players would accept it. And many people prefer traditional assets. And some even hate anything ai, wether their specific arguments are flawed or not, does not matter.
An ai hater probably would not touch a game with ai made assets, even if those assets were generated with a model that is 100% consented material and run locally on a low energy device. The same way a vegan probably would not eat carrion or wear shoes made out of said carrion's hide.