For any crew position in the maritime world, the medical requirements for any position classed as a "Seafarer" include a vision aspect. A "Seafarer" as per the Maritime Labour Convention is defined as:
A seafarer is any person, including a master, who is employed or engaged or works in any capacity on board a ship and whose normal place of work is on a ship.
Would seem to indicate that yes, someone in a culinary position whose "normal place of work" was a ship would count as a Seafarer and therefore be subject to the same medical requirements as anyone else on the crew including the vision requirements.
These requirements can be found in Appendix A of this document
You may not need to worry however since:
a) the vision requirements are not 20/20 (although individual operators are free to apply more stringent requirements than those required by regulations)
b) if your eyesight falls below the minimum for the seafarer certificate you can be issued an ENG1 certificate with the restriction ‘not fit for lookout duties’. Such a certificate means you can technically do things like being a chef and it will then be up to the company operating the ship whether they accept candidates who have this exclusion.
The best course of action at this point is to ask your manager if the "failure" is going to be an issue.