It's not that they know nothing about games; it's that they know just enough to be wrong. Ever go to a game forum and notice how every player thinks he's better than the designers? That combat would be perfectly balanced if the developers would just change that +2 to a +3 for his class? Now imagine that those people are running the business, and you have a pretty good idea of what the problem is -- creating a perfect game looks easy from the outside, in the same way that from the outside it seems like it'd be really easy to make a snake. And those outsiders are in charge.
So why not just have the money folks focus on the business end of game design and let the actual designers do the designing? Well, it turns out "the business end" includes deciding how many hours of content are in the game, whether you have linear progression with lots of levels, how the DLC is going to work, whether powerful items get sold in the cash shop, whether the game is a first-person gritty realistic shooter with RPG elements or an action RPG with gritty realism and lots of guns ... basically, everything that matters. The people who have the most experience and actually know what they're doing are basically just polishing the ideas that the execs come up with.
"New memo, guys: We're working on Call of Duty: Fuck Canada now."