We have all been on the streets enough to hear "Call of duty is dumb just point and shoot". What genre typically then do you feel requires the most out of our brains?
Perhaps you're right Cthulu lord of the deep. I think RTS games requires some QUICK thinking however. You can have hundreds of units at one time, you have to keep track of your resources, the entire map, your enemies armies and his resources. When battles occur it can get pretty hectic to and games can change instantly depending on what's going on.
Fighting games will forever be the games that take the most thought. The practice, preparation, knowledge, and execution standards are all higher than other genres. You have to be not only extremely knowledgeable with your own character, but you also must know the strengths and weaknesses of every character in the game. It's such a fast-paced genre, that it's often deemed to be "too hard to get into." During matches, there's no down-time, and you must figure out the best move to do in the specific situation and also execute said move (which is almost always the harder of the two). The margin of error in fighting games are so small that often you'll (easily)lose 25% of your health simply from double-tapping a direction at the wrong time, and get your movement "punished." And in some matches, you'll lose the entire round from as little as 2 mistakes.
If you're serious about fighting games, you'll easily spend 250+ hours in practice mode alone.