This was a well-designed study with a control group. The group that was not treated for sleep apnea did not lower their golf scores, whereas the group with patients who were treated, did lower their scores.
What is most revealing in this report is that the authors are speaking directly to the reasoning behind such a process. If you want to play good golf you don't want to be tired, you want to be clearheaded and you want to be able to use those resources to make good judgments.
That's exactly the reason they would speculate as to why some of these people did improve their golf scores. When you have a sleep disorder, you are cognitively impaired to your attention, your concentration, and your memory. These are all things needed to play a good game of golf. Moreover, additional to playing a bad game of golf, the experience in itself would be less enjoyable.
I can not guarantee that CPAP therapy would improve your golf scores, but I can say from personal experience that the game of golf is a much more enjoyable experience due to increased levels of energy.