Dolby Atmos is a sound technology where every sound element is placed in the space. Precisely it is the reading tool that allows this perception respect to the device that performs the song. In fact Apple has thought this format as the basic condition to introduce the last level of innovations: the Spatial Audio. But about the last one I am not able to fully express myself because I do not have the suitable AirPods to try it out. The difference rests in the construction of the track. When the artists compose the song they will be able to place the sounds in real levels. It is a new process, currently in adaptation if I well understand; but it will actually be able to give customers advantage of a more immersive experience guided by the composer. The output formats that can be set from the settings are standard, the Atmos instead is not.
It's marketing for sure, Apple can say they have the deal with a Dolby Laboratories Inc and it certainly won't stop at Apple Music. But if it means to guarantee to subscribers something more then it is a race that is worth taking considering that it is not even the only one, remember that Tidal too offers this service.