I have a background in instinctive shooting and would enjoy discussing it with anyone interested, in order to provide helpful information to those who want to understand instinctive shooting.
I think instinctive shooting is boils down to how you assess where your arrow is pointing. There are different ways of doing this. I've seen people shoot blindfolded, so unless they are peeking (LOL) for them it'a all about memory and I am guessing they rely on the feel of where their arm is.
I have been shooting compounds and recently got tired of using my sight. I found that I was getting tense trying to hold my pin perfectly still and on the x. It got to the point that I wasn't really enjoying as much as I used to. So, off with the sight, still using the same compound but now I just try to look where my arrow is pointing. I scan the entire length of the arrow to assess its trajectory. Just looking at the tip doesn't give enough information. Right to left is easier to get right than vertical, but after while it all falls into place. I find this kind of shooting to be more relaxing. I get more shots in also because I'm not aiming nearly as long.
Honestly though, I don't know if what I am describing falls under the proper definition of instinctual.