Psychologically the chef would have felt inconvenienced in returning to the ship, so took a short-cut by stepping from the quayside to the swimming platform instead of using the gangway, which was longer, causing the injury. The chef’s haste and focus on collecting the forgotten item were both distractions, and he either did not notice that the deck was wet or did not pause to consider that this could make it slippery to walk on.
Although the reporter does not say which side of the vessel the chef fell in from, unless they had slid the entire breadth of the vessel, they likely fell between the yacht and the quayside, where they could have suffered severe impact injuries or even crushing.
The superyacht industry is very focused on image and dislikes having areas of the yachts roped off while the teak decks are treated; as the stanchions are removed while the decks are treated, it is anyway often not possible to rope areas off. The gangway should always be the only safe means of access to and from a yacht.
The chef was unaware that the work was taking place. This should have been briefed to all the officers and crew at the daily work planning meeting.