I've given this thought for some time and annoyed I don't see the right answer here. Howling into the wind, there's a logical and truthful reason why the Apple Watch is square and why a circular display would be the incorrect decision. The reason people associate watches with circles is because they are small wearable clocks. This technology and machines have traditionally been circular to accommodate the visual communication of time displayed by mechanical hands in a circle. That wouldn't be best communicated with a square, or a rectangle, or a triangle or whatever shape you please. So clocks thus watches are round.
The Apple Watch is not a clock... It is a computer. There is a difference. This technology and machine have traditionally displayed digital data. This could be the time, or weather, or the sports score. This digital data is best displayed in a square display as it may contain not only the time but text and visual icons. When displayed in a circle, and I'm sure Apple's prototyped this to death, this digital data appears to be cut-off or partially show or shrinking in the vertical space. This does not best communicate this digital data. The very idea of a circular smartwatch display is contradictory to the use it provides.
You may like or prefer a circular display, and okay whatever it's just smartwatches, but if you're designing and making one to be the absolute best, which Apple does, it would be square.