When we speak of wearable devices, we are overwhelmingly referring to smartwatches, and a watch that does not tell the time isn't really much of a watch. It's like having a luxury yacht that features state of the art GPS technology but has trouble staying afloat. To strike a metaphor closer to home, consider a smartphone that has trouble functioning as a phone. (Wait! That's actually happened!)
The term watch face is used to refer to the digital display of the current time on the wearable device so that the user can tell at a glance what the time is, in much the same way one does when wearing a watch.
Unlike a traditional watch, however, our wearable has a multitude of additional functionalities restricted only by its own internal memory and its communication with one or more paired handheld companion devices. So, showing the time on a wearable speaks to a far more sophisticated piece of software than, say, software that is written for a digital watch...