Many people think a dominate eye sees better or faster or whatever, but that's not quite the case.
The dominate eye provides slightly more visual data to the brain, due to more neural connections. So it becomes the leader (for lack of a better term) when it comes to processing what we're seeing. But "more visual data" doesn't necessarily mean better visual data.
Each eye converts light signals into images, then the images are sent to the brain to make sense of it all, to give us a visual perception of what we're seeing. Even though the brain receives image data from each eye, it relies more on the data provided by the leading eye, rather than the non-leading eye. The end result is a visual perception created through preferential processing.
Eye dominance is similar to how the brain tends to favor one hand over the other. At first, as a child, we typically develop a favorite hand to use for doing things, which could be for the simple reason that that's the hand we see our parents or siblings use most often, so we start using one hand more than the other. This allows that hand to create more neural connections with the brain, which leads us to becoming right-handed or left-handed. The brain then prefers that hand because there are more neural connections involved.
The odd thing is, unlike right or left handedness, eye dominance can actually shift from one eye to the other depending on what we're looking at, the varying distances and sizes of objects involved.
Of course, none of this makes a difference when it comes to playing pool. I mean, knowing this stuff doesn't help one bit if a player is struggling with trying to see the shots right. I just think it's interesting.