I doubt I had any concept that math might be game-like when I was struggling with it in high school. I was just overloaded by the unfolding system, and had no guidance at all on math's philosophical status.
Music might be analogous, but I'm not sure I find the atonal stuff particularly musical. I suspect that the meaning and emotional impact of music have to do with its underlying metaphors. A song stands for a life, the melody for a personality or for the plot of the story.