[ That sound is actually replicating an older analog camera, not a digital one, but I digress ... ]
It doesn't always play for me either. Sometimes you won't hear it when you are switching from Video to Photo by pressing the shutter release, at least for the first shot, but will hear it on the second shot. Just take two at times like that to be sure. The answer here is to switch from Video to Photo via the on-screen icon first before taking the photo, rather than making the switch via the shutter button.
I have once or twice experienced it going away for that flight. I'm not sure why that happened, but that could also be something to do with your device (phone / tablet) and not the aircraft / controller.
Chris