Well put. The article makes it sound like training the "quiet eye", i.e. improving eye focus by X percent, will improve elite athlete traits of calmness and zone/flow. When cause/effect operating in the opposite direction is equally (if not more) likely.
Disclaimer - I wrote the article I'm genuinely interested in your point here, but doesn't the research on quiet eye training actually support this causal link? Lots of the studies showed that feedback on the athlete's eye movements does improve their accuracy, better than control interventions that did not explicitly teach the quiet eye.
As an aside, do you know of any research where eye movement is not possible? I'm thinking of sparring in grappling, where you can't see parts of your opponent's body because you literally can't move your head that way.
