In this context game directors are the leads in charge of game systems; they answer to the director, or project owner.
Directors are the leads in charge of the project, aka Project Owners; they answer to CEOs & chief financial stakeholders.
I'm sure there was a lot of sharing of responsibilities... but there's a reason 1 person got the "Directed by" credit.
No, 'directed by' means 'game director'. 'Director' means 'game director'. 'Directed by' means 'director'. All 3 terms mean the same.
They set the direction of the game and the gamedev team. They are the bosses of the directors of each department/specialty telling them what and how they want to do each thing. There can be programming directors, art director, cinematics directors, animation director, audio directors, creative (design + art) directors, narrative directors, design directors, level design directors, combat directors and many others who are the ones in charge of their areas. These department directors have several leads under them, sometimes more specilized than them with stuff like lighting, character art, environment art, rigging, level design, network programming etc. And under them seniors, juniors, trainees, etc.
Then there are the producers, in charge of organizing the tasks that all these people has to do, follow their progress, help to solve blocking issues that may appear, trying to make sure everyone has something to do, making sure they have enough resources and tools etc. to help having the stuff done to reach milesones on time and on budget.
But it depends on the studio (specially depending on their size) and the game. Some studios don't have game directors, other ones don't even have department directors. Some other ones don't even have leads. Some don't have producers. Producers typically have nothing to do with the game direction, but in some studios where there aren't directors they take that role too.
Then there are the product managers. In the same way directors and producers are in charge of game development, they are in charge of marketing, communications, PR and customer support. They basically make market research and provide what sells and what not, what players and gaming press like and what not, make playtests, focus tests, providing data as tools for the dev team to decide their stuff, etc. Then they also make the marketing and PR campaigns etc. In the big AAA IPs typically as boss of the product manager there is a brand manager, in charge of the series, the whole IP, instead of only a specific game.
In many studios in charge of the game there's the product manager, the producer and the game director (sometimes named Creative Director, but in some studios the creative director is a department director in charge of design + art who works under the game director) and other studios don't have creative directors.
Nah man you're literally dead wrong.
I've been working as gamedev since more than a decade and a half, some of these years in a top 5 AAA publisher and have many friends in multiple studios from different top publishers. I know what I'm talking about.