Hey Hellfire,
I don't blame you for being confused, its not exactly clear in many cases. Sure, we all know major names like Kojima, Will Wright, or any of maybe a dozen (maybe) individuals we can point to, but that's not the whole case. They are the exception, not the rule.
Though it works differently at different companies, the two people who know the most about an individual game on a day to day basis are the producer (product development) and product manager (marketing). The producer manages the development team and is the unifying element that guides the product from concept to release. The product manager does a similar task, but focused more on the market itself and packaging, promotions, sales, and advertising. At companies where the process works, the producer and product manager are in constant communication, discussing the title and making sure everything is on track.
The position you are thinking of (creative director, head of product development) exists at some companies, but it is one of the hardest to achieve at any company, unless you start your own. Everything you do in this industry has to do with what you did previously. The producer track is the common approach to attaining this position.
That being said, ideas are solicited from almost everyone at a company, and who knows when your lucky break could happen. At every company I've worked for, internal requests for game concepts occur. You might not be on the team that makes the game, or ever work on it past giving your idea, but concepts come from everywhere.
Everywhere inside a company, that is. Due to legal reasons, no company will hear a concept by an unknown. If you have on paper something we are currently working on and we agree to hear it, you could sue us. For that reason, only established companies with more than just a concept on paper actually get in the door.
In the case of Kojima, he basically does whatever he wants. If he wants a game to have a certain title, he gets it, whether or not the title totally makes sense (guns of the patriots?). If he insists on new features, he gets them. He focuses his efforts on the main franchise, Metal Gear Solid, but also controls an entire studio, Kojima Productions. He is not the creative mind behind everything that Kojima Productions does, per se, but his mark is left on each and every game they release. His position is best described as "Game God" and as I said, only about a dozen people in the world have that much power.
Okay, I know the above is confusing (I warned you), let me know if you need me to clear anything up.