I don't think it's a matter of achieving a faster reaction time by bypassing higher brain functions. It's about looking several steps ahead and planning out multiple steps before you need to do them, and then anticipating when each action needs to happen.

One game that really demonstrated this to me was Crypt of the Necrodancer. It's a rougelike where each turn is the beat of a song, and the tempo of the song for each floor is slightly faster than the previous floor, starting at 120 bpm (1/2 second per turn) on floor 1 and topping out around 180 bpm (1/3 second per turn). For the slow songs, you have enough time between beats to fully plan your next action, but at some point, as the tempo gradually increases from floor to floor, you hit a point that this is no longer possible, and your brain has to "switch modes" to planning several beats ahead and thinking in patterns instead of individual moves.