I remember reading, decades ago, that the U.S. Navy's flight school in Pensacola had a student who'd done unusually well in the course because he'd bought a copy of an early version of Microsoft's Flight Simulator software (IIRC) with maps of the nearby Navy airfields used for student training. That led to the Navy adopting PC-based flight simulator software generally. (I couldn't find a reference.)
The book is Sink the Rising Sun.
The TDC is described well here - https://en.wikipedia.org/wiki/Torpedo_Data_Computer
Manual for the banjo here. Imagine a slide rule that could solve the problems in this game (given perfect input data) - https://maritime.org/doc/banjo/index.php
I love reading about physical tools made to solve very specific computational problems. Beyond all kinds of weird-shaped, weirdly-scaled, often circular-ish slide rule variants, this includes also all kinds of charts that are effectively currying a complex mathematical function into something with 2-4 parameters and plotting them over useful range, so you can quickly read a specific result for a specific situation.
On the one hand, this is a relic of times before general-purpose computers; today, you'd just code the equations up and even automate their use. On the other hand, those physical artifacts usually have superior UX, especially if the computer equivalent would require you to input any data. No surprise these things keep showing up in the history of high-stakes endeavors, whether it's submarines or battleships or space orbiters.
Can't you get the bearing and range with passive listening from two points, and/or single point but measuring over time?
As for why not to confirm a solution with active sonar before firing; if what you described are rules of the game, then IDK because it doesn't seem to load anymore. In real life, I imagine an active sonar ping being much clearer and more informative to the enemy than the noise generated by launching a torpedo.
We love our wargamers don't we folks