Like everything in software engineering the answer is depends on rs
No silver bullet, as you said Brooks, then there is no "equivalences", why these practices/documents you quoted are not exclusive to "systems".
In addition, a game is also a software. So, what prevents a game from adopting one or more of these practices? Absolutely nothing.
You cited various practices at different levels of abstraction, which makes the question very broad and makes it difficult to answer "exact". Also, why is it not useful to have a game technical specification? And why not coding standards and standards for design? Again, nothing prevents the application of one or N ES practices in game development.
Specifically as to your question:
What is equivalent to a functional specification for games?
Nothing prevents use cases, user stories, business models with their rules, etc.. However, due to some specificities, it may take a lot of work to document only with practices better known by the market "conventional".
In the case of games there are also widely accepted practices. An example:
- Game Design Document: with GDD it is possible to represent various aspects of a game as technical (class and components, for example), graphic design and also functional, such as game history (how to achieve goals, for example), your characters, etc. There is a lot of reference and examples about GDD on the web, maybe it helps you.
Another consideration of another question:
There are formal tools to make it clear the goal to be achieved?
Well, you can put any practice in a formal method in ES. If it is always functional and is necessary, there are already another five hundred.
Finishing and remembering, there are no rigid standards in ES, you can adapt existing practices, compose your own mindset, evolve according to your needs and always go beyond =)
I gave +1 for contributing the question.
– jlHertel