It doesn't use e-ink. It uses a Sharp Memory LCD (http://www.sharpmemorylcd.com). I think Pebble calls it e-paper because they promised e-ink in their first kickstarter but were unable to deliver on that. No one else calls it that. I assume a custom e-ink display was too expensive. The first Pebble used the same display as one of the early Nike watches, which made it a lot cheaper.
The original Pebble uses a Sharp LCD. The Pebble Time uses JDI display. I have no idea what display the Time Round uses: do you know for sure it's a Sharp unit?
I'm not positive they still use the Sharp brand, but I'm pretty sure the display technology is the same: LCD backed by SRAM in the display. You don't need to continuously update the display. Once you write a frame or part of a frame, the processor can go to sleep.
Given that they claim 10 days of battery life for the Steel, maybe we should expect the Round, which has a claimed two-day battery life, to only get one.
