Do the other attendees on a meeting have to be Clockwise users for Clockwise to take their availability into account when rescheduling?

No. Due to the way Clockwise connects to domain calendars, Clockwise can tell when the other meeting attendees are free or busy, and only moves meetings into time slots when they are free. Clockwise infers meeting hours of 10:00 am - 4:00 pm, Monday - Thursday, and 10:00 am - 3:30 pm on Friday in the attendee's local time zone.

If the attendees are Clockwise users, then the meeting preferences of that attendee can also be taken into account (when they get into the office, when they eat lunch, etc).