You're right, of course, it isn't a watch. It's a tiny computer strapped to your wrist. Unfortunately few people want to buy a device described as such so it makes more sense to market it as something people can vaguely remember using.
As for the power issue people used to wind their watch every day. Alternately, if they gave it a low enough power screen (like Pebble[1] or something) they might be able to charge it from the motion of the users wrist.
[1] Yes I know pebble uses an e-ink screen and Apple is unlikely to follow suit.