Nope it means he works in the ships engine room, any ship. However, he is according to the story assigned to a sub; just has qualified for his silver dolphins to wear above his two ribbons yet.
Actually, he’s an Auxillaryman. They combined non-nuc Machinist Mates, Torpedoman’s Mate and Internal Communications Electricians into one rate years ago. He’ll see plenty of time in the engine room though working on quals and cleaning bilges under the lube oil purifiers...