Curate, connect, and discover
I've said that organizational dysfunction should be a villain more often, mostly because of my belief that we need stories that give us information about how to deal with the biggest actual problems we, as a society, face. It's just very hard to write a story about organizational dysfunction that includes actually beating the organizational dysfunction.
But there's one place where organizational dysfunction does have an opportunity to show its villainous nature: videogames. Specifically, management videogames, where making decisions about organizational goals and who to hire is already central to gameplay.
Now, the average "management" game is not really about management per se. Everything is hyper abstract, you have a god's eye view, and you have ultimate authority over everything that you do. You are still looking for weak links and problems to correct, but a lot of that is pathing issues (if the game has that) or restructuring physical space.
So a management game that's about organizational dysfunction would be one where you're the new boss, looking to right the ship, and it would need to be an opaque organization, one where you can't just look inside someone's mind and see the "takes credit for others' work" trait.
I guess when I put it like that, I'm imagining something that's more like a detective game, as you do interviews and comb through piles of documents. And it's not as simple as "fire the bad people", because often those people are pulling a lot of weight, that's one of the reasons they've stuck around for so long, and replacing them is genuinely a hit to the company's ability to do ... whatever it's trying to do.
(Definitely also possible to do this same thing set in a government agency, a non-profit, or any other organization, though the actual problems will look at least somewhere different.)