The word "verisimilitude" as far as I know may have either been popularized in the field of philosophy or art, but the common and loose meaning of it is:
2. Something that has the appearance of being true or real.
American Heritage Dictionary
1. the appearance or semblance of truth or reality; quality of seeming true
In Merriam-Webster we have:
1:the quality or state of being verisimilar
With "verisimilar" defined as:
2:depicting realism (as in art or literature)
Here is a note at Merriam-Webster online about "verisimilitude":
From its roots, verisimilitude means basically "similarity to the truth". Most fiction writers and filmmakers aim at some kind of verisimilitude to give their stories an air of reality. They need not show something actually true, or even very common, but simply something believable. A mass of good details in a play, novel, painting, or film may add verisimilitude. A spy novel without some verisimilitude won't interest many readers, but a fantastical novel may not even attempt to seem true to life.
Note, that in philosophy it means something more specific, and has a lot to do with the philosophy of Karl Popper. However the word itself in English dates back to about 1600, with the meaning of:
"appearance of truth or reality, likelihood,"
"likeness to truth,"
Online Etymology Dictionary: verisimilitude
Regardless of the fact that many will insist it's meaning is strictly that as used within philosophy, or even the second definition given by Collins:
2.something that merely seems to be true or real, such as a doubtful statement
That is, much like "sophistic" or "specious" (appearing true, but not) I don't think anyone would doubt that it's commonly and simply used to mean "realistic seeming/looking", although arguably it may just be a longer and more obscure word for "realistic". In any event, even if we take that meaning, the "appears to be true or real, but isn't", I think that actually matches your case, because you are "simulating" reality, and it isn't really real.
Edit: I've reread your question. Since what you're trying to do is a "simulation", that's probably the best word to use. You're right, Battleship is very abstract, that's why no one would call it a simulator. If a game, such as a board game you describe, is called a simulator, I think most people will expect it to be historically and militarily faithful to real-life (realism). In games some level of realism is usually sacrificed for playability and enjoyability, but I don't see any better way of emphasizing how real it is without using "simulation" along with some modifying words and description.