The rangefinder does not communicate with your headphones, it communicates directly with your mobile phone and the supporting rangefinder app. The app in turn is what generates the calculations and verbal information similar to as you would listening to music or a phone call on your headphones. All the range finder does is provide distance and angle then communicates that info to the app and the app works out the rest.
Keep in mind however, before you go hog wild with this unit out in the field you may want to check the hunting regulations in your area if you plan to use it to hunt legal game. Here in Minnesota for example wireless devices of any kind are prohibited while hunting with the exception of a wireless dog collar for dog tracking purposes if I recall correctly. Even if you are not using your phone while hunting but have it on you and you have a run in with a dnr officer you are likely going to find yourself on the receiving end of some hefty fines or worse.
So be certain you want to pay the hefty price tag for this unit if you are planning to go hunting with it because there are less expensive options out there that don't require a mobile phone to access the full features this unit provides should your area ban wireless devices while hunting. I haven't looked lately but they used to go for approximately $400