It would be nice if a person actually trained in sports vision analysis could join the conversation. But, in the absence of such a person....
I think the main use of two eyes at pool is in depth perception, which presumably improves your feeling for the cut and carom angles.
On the other hand, one of the greatest players of all time, Joe Davis, had only one eye that was useful. He shot pretty well on a snooker table.
An interesting experiment would be to use eyepatches on both veteran players and beginners, but a tough one to set up. Most people are used to using two eyes and it would probably be a large hurdle for them to change to one.