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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.’

plausible TFD

1. Seemingly or apparently valid, likely, or acceptable; credible:

As in:

"The Great War at Sea" series of games goes much much further, providing a more plausible simulation of the real world.

naturalistic

Having the appearance of nature or realism; lifelike or realistic. (Wiktionary, 2019)

And

Naturalistic art, literature, acting, etc. shows things as they really are. (dictionary.cambridge.org, 2019)

A naturalistic game more closesely represent the natural world as opposed to an abstract world.

Board game fans use the word "crunchy" to describe a game that has highly detailed rules for simulating something. Crunch is complemented by fluff, which is non-binding descriptive text.

Since board games often simulate things that don't exist in the real world (such as magic or fantastical technology), the world "realistic" doesn't necessarily apply. Rather, "crunchy" refers to how detailed the rules of the simulation are. Crunchier games typically demand a greater investment of time and brainpower.

Further reading: https://ludobits.com/terms/crunchy/

In games, simulation itself is often used to refer to games that attempt to accurately render reality, as opposed to abstracting elements away where they won't interfere with the players.

This answer is somewhat dated and culturally-specific, but in the field of simulation gaming (and war gaming in particular) a game with a very high level of detail was at one time known as a "grognard" game.

Your request is very specific, in that you want something that expresses the idea of the accuracy of the game's approach to simulating real life. I don't think you're going to get a single word for this, and I would suggest

simulation authenticity

I think that conveys what you want--"authenticity" by itself could refer to historical background in the game text, or how realistic the art is. "simulation" on it's own doesn't say what you want them to judge about the simulation--is it consistent? Does it feel balanced? Is it smooth computationally?--any of those could be ways to judge "simulation".

You need more than one word to say what you want them to judge (the simulation), and what about the simulation you want them to judge, which is the realism or authenticity of the simulation. So I think, as above, simulation authenticity or a variation on it such as simulation realism is as good as you're going to do here. As a judgement category, realistic simulation (like, on a scale of 1-10, was it a realistic simulation?) might also work.

The phrase typically used in the context of video games and trainers (e.g. flight simulators such as DCS, Falcon BMS, and the like) is full fidelity, describing their attempt to simulate the experience of the pilot in every way except physical in terms of interaction with the world and the cockpit. In the context of these games this includes a fully functional interactive cockpit and aircraft computer systems, and a realistic world to stage combat missions in.

This is an exceptional degree of realism that is probably beyond the scope of a board game in most cases, so a more accurate word might be authentic, often used by video games that attempt to provide a close approximation or sense of reality without intending to be truly realistic, such as the Arma series. It has the connotation of being true to real life without implying that it is attempting to reach the highest possible degree of realism in terms of details.

In the board game industry, the standard way to describe a game that is the opposite of an abstract is to call it thematic. Thematic games tell a story, present a detailed setting, and often focus on delivering content and characters and events rather than a set of elegant rules.

For example, chess is an abstract game. It's said to represent a war, but it's represented in a very abstract way. It doesn't tell an explicit story, it doesn't have setting or character or try to simulate things in detail, but rather presents a set of simple rules within which players compete. Now compare this to Axis and Allies, the popular WW2 board game. It features different kinds of units, industrial production, economic considerations, research and development, etc. Risk is a war game that's somewhere in between.

The game you're talking about you might describe as "heavily thematic" because its first design priority appears to be to accurately convey the world it purports to represent (much more like Axis and Allies than like chess) and sacrifices a certain amount of accessibility as a result.

References

1. https://boardgamegeek.com/blogpost/31990/litmus-test-thematic-vs-abstract-game


2. https://boardgamegeek.com/thread/1315704/thematic-or-abstract


3. https://boardgamegeek.com/thread/1179217/abstract-vs-themed-false-dichotomy

mimetic

mimetic (mɪˈmɛtɪk) or mimetical

adj

1. of, resembling, or relating to mimesis or imitation, as in art, etc
2. (Biology) biology of or exhibiting mimicry

https://en.wikipedia.org/wiki/Mimesis

Mimesis (/mɪˈmiːsɪs, mə-, maɪ-, -əs/;[1] Ancient Greek: μίμησις mīmēsis, from μιμεῖσθαι mīmeisthai, "to imitate", from μῖμος mimos, "imitator, actor") is a term used in literary criticism and philosophy that carries a wide range of meanings which include imitatio, imitation, nonsensuous similarity, receptivity, representation, mimicry, the act of expression, the act of resembling, and the presentation of the self.[2]

Somewhat colloquial classifications would be "spot-on" and "right on the dime". While they do not formally define the game as a simulacrum, the implied metric does not make sense outside of an emulative context.