It has been standard in the towers I have worked with more than one local controller to announce go arounds throughout the tower. The local controllers are working independently due to procedures that establish standard separation without coordination.
Obviously, go arounds are not standard, and usually do not conform with the procedures established that allow the multiple local controllers to work independently. For example, when the local controller responsible for only arrivals to one runway has a go around, he essentially now has a departure on his hands. It's important to coordinate with the local controller who has responsibility for the other departures off another runway. The BBC clip was an excellent example of this scenario.
For towers with one local, there may be reason to call out a go around if there is a tower cab coordinator who would need to coordinate for local if he was too busy to do it himself. The call outs in these examples are for the benefit of the other controllers, not the pilots. We just happened to catch the call out in the background on the local controller's transmission. Like tyketto said, if the reason was for wind shear or FOD then a general transmission would be made to inform the approaching aircraft.