It's not unusual for new technologies to drag along some of the design elements of the old - computers have keyboards just like typewriter keyboards even today - but most do so only out of habit and then abandon those elements that don't work fairly quickly. For example, television shows were originally treated basically like radio shows with video or a televised version of theatre but quickly expanded into a far more dynamic, cinematic medium.
I put the trend towards round smartwatches in this camp. The vast majority of what any computer screens display is predicated on the rectangle - lists, photos, buttons, paragraphs, characters and pixels... The entire user interface is based around them.
This, in turn, is because most of what we do also trends towards rectangles - pages, screens, boxes, keys, laptops, paper notebooks and characters of text (as empathised by any government form you may fill out).
Some user interfaces can be made circular - buttons can be round and progress bars can curl around a circular path - but it's clear that we tend towards the rectangle in how we work and how we think. Yet, we have small wrist mounted computers with round screens. It makes sense only in one context - the watch face. The clockwork sweep of the hands is a circular motion.
To be clear, I like the look of the round LG smartwatches, for example, but consider it to be a clear case of form over function. A round face is attractive but not useful. It is a wasteful affectation that benefits one facet of the watch and hobbles the rest.