This seems like a very poorly designed study. Their metrics don't do a great job of measuring what they purport to measure. Even a dead person can "influence the outcome of events", albeit not actively. And besides, anyone who believes in an afterlife (or even really a soul) is likely to suggest that David can still "be aware of his environment, possess a personality and have emotions."
For your consideration, a psychology study as summarized by The Economist in "How dead is dead? Sometimes, those who have died seem more alive than those who have not":
The study is "More dead than dead: Perceptions of persons in the persistent vegetative state":
Ed Yong points to another interesting study, the 2004 "The natural emergence of reasoning about the afterlife as a developmental regularity":
Jach on Hacker News makes the obvious connection with cryonics; see also lukeprog's "Remind Physicalists They're Physicalists".