Why "Story Rich" and not "Rich Story"?

It's an adjective. A "story-rich" video game would be one that focuses on having a complicated plot. That really needed to have a hyphen. 

The tags are (usually, if not all) written as adjectives. ‘Story-rich’ is an adjective. For example: “This is a story-rich game” Meanwhile a ‘rich story’ is a noun. For example: “This game has a rich story”

“Story rich” is an adjective phrase where as “rich story” is a noun with an adjective modifying it. For example, “The game is story rich.” As opposed to “The game has a rich story.” Edit: Steam tags could use either and it would be fine, but that is the difference.

Story rich means that, (in this case the game) is “rich” in story. It has a lot of story or a lot of stories. This could mean that there is a lot of detail to the plot, or it could also mean that there are a lot of different stories and narratives to follow. A rich story means one specific story that is good and full of detail, emotion, nuance, etc. For this example I’ll use Red Dead Redemption as a story rich game and The Last of Us as a rich story game. RDR is an open world game with a lot of characters and details to uncover. There are a lot of side missions and unrelated events that are all their own story. There is also an overarching plot to the whole game. It is rich in stories. TLOU is a pretty linear game. The events happen one after another and while there is exploration and side characters with their own stories, it’s very limited and mostly related to the main storyline. It’s a rich story with a lot of detail, emotion, and narrative but it is still just one story.

Also importante, "Story-rich", Is describing the game itself, while "rich story" describes the story The game Is story-rich (this game has very good/a good qantity of, stories) This story Is rich (the story Is very good)

You can do it with almost any similar noun-adjective combo that makes sense as well: calorie-dense, cheese-laden, microwave-ready, constipation-inducing... drug-addicted... Man, all out of drugs and apparently I'm getting hungry.

As others have mentioned it should be hyphenated here to be used correctly which adds to the confusion. I think Story-Rich is different from Rich Story because Story-Rich can have many stories, while Rich Story typically would be one story that is considered Rich.

"Rich story" would mean that the story itself is rich, or very good. "Story rich" is saying it has a lot of story. Compare it to The Lord of the Kings vs Battlefield Earth - the former has a rich story, the latter was written by a hack who got paid by the word.

A game can be story rich, but have a poor story.

So, it would have a nuanced difference in semantic meaning to do one over the other. "Rich Story" means the story is rich in some fashion. The game might not have the story so tightly integrated but the story itself would be really detailed. By saying that the game is "story-rich", it's saying that there are a lot of integrations between the story and the events that happen in the game. Metroid Zero Mission has a rich story. But it's not really story-rich. Metroid Prime on the other hand has a rich story and is very story-rich as there's tons of lore to read that gives background to what's happening in the game. Metroid Prime 2 is even more story rich because you interact with the inhabitants of the planet and their post-mortem holograms and they give you some exposition in addition to the lore you can read from them, the Space Pirates, and even Federation Troopers.

"[thing] rich" is a phrase to indicate there is a lot (possibly too much) of the thing.

"Story Rich" Is a tag used on Steam to contrast games that don't have much focus on a story at all as some games are much more focused on gameplay rather than story.

Story rich means it is rich in the amount of story it has - it has a lot of story. Rich story would mean the story itself is rich or has a lot of value.

Story-rich means it has lots of story, rich story means the story itself is well-developed.

It's "Story Rich" because its a user-defined tag and apparently the user that defined it didn't care about grammar. It should have been either *Story-RIch* or *Rich Story*.

"Story rich" = Rich with stories; in other words, there are a lot of different interesting narratives within the game. If you've played any Rockstar game, they're generally filled with lots of smaller questlines that deviate from the main storyline. "Rich story" = The single story is rich.

Like some of the other folks say, its being used as an adjective rather than a noun, because it's being used to categorize multiple things not describe one individual story.