A watch is not a monitor. Nobody wears a TV or computer display on their body, much less their arm. People are not reading and writing documents and working on spreadsheets and databases on their wrists.
That said, I think Apple did exactly the right thing to get developers on board. They went square to make it easier for developers and themselves, despite so many of their graphics being circular in nature. Now that they've established the watch they can focus more on fashion as a choice. Rounding those corners sets it up perfectly to fit into a round format -- offered solely as a fashion choice in addition to the square for those who use the watch more aggressively. For most things round is perfectly adequate shape to present notifications, and brief text messages. Some people would rather not read a lengthy email on a 42mm screen on their wrist anyway.
Here's a few examples that show that there's really not much difference between presenting the same information in a round form. As I pointed out above, the graphic I use for example purposes is an actual 42mm Huawei Watch, using the same scale as the 40mm AW S4, which has actually had an edge-to-edge display with a smaller bezel since the AW S0, as the comparison below demonstrates. Apple even enlarged the display area from the 38/42mm (brown) to the 40/44mm (orange), but did not shrink the bezel as much as the Huawei has had for 4 years (rust).
First I've included a straight up match, the 40mm displays scaled to the 42mm Huawei. Then I present an "optimized" version to better fit the round design, along with the larger display area.
Note also, that even the screenshots have the same rounded corners, even the iPhone X doesn't do that. It's not a lot to go from there to round.
Apple even introduced guidelines for designing within rounded corners:
https://developer.apple.com/design/human-interface-guidelines/watchos/visual-design/layout/
Once they go down that path, it's really not a problem to go all the way round. Again, this was NOT something the original Apple Watch developers had to contend with. Now there's a thriving user base that makes dealing with these headaches worth it.