How to disable mute on focus lost?
Muting like this is done by the application itself, not the operating system.
This means if there is no option to toggle this in the the game, then you will not be able to change this. It is possible that the developers want to cut down on resource use, while the window is out of focus, and slow down some of the processes.
Try to put the game into "windowed-fullscreen" mode if possible. This way you can open up a browser on top of it and still possibly see the important parts of the game.