McDave's right. Hand-eye coordination has a lot more to do with sports like baseball, tennis, etc. in which you have to bring some implement, bat, glove, racket, to where the ball is at the right time.
Dan is also right, some people just naturally have more ability at some sports than others - that's what produces athletic superstars - everybody who's playing at the professional level has worked his butt off to get there, but there's no amount of work that by itself will take a good professional athlete to, for example, Michael Jordan status. Some of it's work, but some of it's inborn.
However, part of the pure joy of archery is that you control the shot. You don't have to swing something at a ball, you don't have to throw it any place - you are in complete control of when, or if, the shot is made. Even hunting, you can always pass on the shot if you don't like the way it's setting up.
If you assume good consistent form from the beginning of your draw to anchor to release, and assume that you adjust for distance as per Terry's form clock, at the waist not at the arms, you need a lot of practice to allow your brain to learn how to hit a selected spot at varying distances. You've got the most amazing computer the world has ever known planning your shots. Keep your form consitent, give that computer enough input with practice and you'll be very good.
And yeah, somebody will always be better, but who cares. If you're having fun and love to shoot, that's what matters.