I think it's good.
Obviously, that style isn't going to work in every game.
But I think considering what the game is about, that is, running from death while dying of old age. I think it creates an interesting and foreboding atmosphere.
I will say that it is usually best to have the music to continue playing when dying. However, if your method when dying is reloading the scene, I'm pretty sure there isn't a way to not have the music also restart. Maybe you could have a variable (it might need to be a global variable) which might increase each second and then when the scene is reloaded, it starts the song that many seconds in equal to the number that the variable is. And then have the variable go back to zero when it equals how many seconds long the song is. I have not tried this idea out myself, and I could just be overthinking something very simple like I usually do with my code.
But overall, the music is pretty solid.