What adjective means "accurately representitive of reality"?

The Great War at Sea is faithful to the intricacies of naval combat. / The naval combat is portrayed with a high degree of fidelity.

Faithful in Merriam-Webster:

4 : true to the facts, to a standard, or to an original

a faithful copy

One common collocation is "faithful to the source," referring to an adaptation that keeps key components of an original artifact. A film might be faithful to its source, a book. In this case, the board game is faithful to its own source: military histories of early 20th century naval combat.

Also, I prefer faithful because it aligns well with a noun, fidelity, which denotes "accuracy in details" (Merriam-Webster). In other words, faithful and fidelity describe a level of exactness in detail that seems desirable for describing a detailed naval simulation.

Authentic

1a : worthy of acceptance or belief as conforming to or based on fact. paints an authentic picture of our society

b : conforming to an original so as to reproduce essential features. an authentic reproduction of a colonial farmhouse

c : made or done the same way as an original. authentic Mexican fare

You used the word “accurately” in the title; accurate also works just as well.

1 : free from error especially as the result of care. an accurate diagnosis

2 : conforming exactly to truth or to a standard : exact. providing accurate color

...

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:

verisimilitude
2. Something that has the appearance of being true or real.
American Heritage Dictionary

n
1. the appearance or semblance of truth or reality; quality of seeming true
Collins Dictionary

In Merriam-Webster we have:

1:the quality or state of being verisimilar
Merriam-Webster Dictionary

With "verisimilar" defined as:

2:depicting realism (as in art or literature)
Merriam-Webster Dictionary

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,"
or
"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.

When one says something is lifelike, they mean it looks "realistic" though it is not "real".

"The Great War at Sea is a lifelike game"

ODO/Lexico:

lifelike
ADJECTIVE
Very similar to the person or thing represented.

‘It's a very accurate and lifelike representation, and it belies its shoestring budget.’

‘The characters aren't very lifelike and the game is beginning to drag.’