As speculation grows about whether he would float or not, the victim's physical condition has not been considered.
I've spent a fair amount of time with actively psychotic adults and children, it can be a frightening situation for the uninitiated. When a person is in an agitated psychotic state, their heart rate is significantly elevated, blood pressure goes up, respirations become rapid and shallow. Jumping, falling or being thrown into the ocean will initiate a shock response, possibly causing heart failure or gasping for air. Either might well cause the victim to inhale a quantity of water sufficient to quickly drown him.
Witnessing an active aggressive psychotic episode can be trauma inducing to those witnesses, especially if they were the targets of the person's rage. This experience can easily delay quick appropriate responding and affect rational thought. Under more normal MOB circumstances a trained and experienced Captain should know how to immediately respond. However, no one is trained to deal with an agitated psychotic person onboard a small vessel 300 miles out to sea.
What we do know is the victim had a questionable history of depression or other mental illness, he was on a small boat with strangers, he became extremely seasick and likely disoriented as a result, he was given a prescription medication that can cause delirium and psychosis, he became agitated and violent, threatened the crew, and eventually went overboard.
If the captain made a mistake, it was not returning to port as the situation deteriorated. He had a real emergency and wasn't aware of how serious it was. It is difficult to fault him, as it is likely he did not have the experience or training to respond to a psychiatric emergency. Returning to port as quickly as possible and requesting assistance would have been the prudent course of action.
One lesson to learn here is, don't try to control an agitated possibly psychotic individual by threatening or intimidating. This will only escalate the situation and things will go south quickly.