That's because, at heart, the Great Red Herring Chase is a typing game. (Against type. Typing game. Ho ho ho.)
To the accompaniment of some moody piano music, you chase crims across town using your typing skills. To turn left, you actually have to type "turn left" or "left" or "hang a left", depending on what's shown at the bottom of the screen. Other times you'll need to "hit it" or "do a u-turn" or even order your catch out of his vehicle.
There are story interludes between each chase sequence and, really, it's all rather clever and well-produced.
Great Red Herring Chase [Intuition Games]