Earlier quoted context omitted.
Yes but why would you ever be talking about your left? Use the definite article, THE left, and it should be clear by convention for the sailors. I think it's just historical.
Imagine you are crew, standing on a ship. You are facing east, and the bow of the ship is facing north. It’s night and there is a thick fog. You hear a cry “man overboard on the left!” Where is the overboard person? Are they to your left, the ships left, or the left of the person shouting? If the cry is instead “man overboard on the port side!” there is no question.
This is about as worrisome as "you are the fire department, and you are told you need to rescue some people on the 14th floor. Quick, does that mean you go up 13 flights of stairs, or 11?" Realistically, you aren't getting it right on spur of the moment decision making.