If you're driving a car you are using up energy to do so, in the sense that you are burning calories to move your body to control the vehicle. But the gas burned in the engine is what moves the car. You use energy to control a device that will use a lot more energy.
A CPU is just many many electric circuits, inside of all of those circuits charge flows across potentials, hence power is dissipated. Your CPU consumes power, and then uses it up to generate $0$'s and $1$'s. But those "control signals" then go to other elements, like a monitor, memory, speakers, and those also consume power by virtue of charges flowing across potentials.
Thinking about it in terms of "work" can get tricky. If a ball is dropped, does the earth do work to accelerate it, or does the balls potential energy just become kinetic; both are identical statements but it is all about perspective. In a certain sense the entire computer is a closed system and all the work is done by the wall plug. In another sense your entire house is a closed system and the work is done by the generator. It makes much more sense to think of these things, weather it be a CPU, a driver, or a highway as systems transacting energy as opposed to doing work on each other.
Almost identical to the example of driving a car. The "control signals" you generate cause other elements to use a lot of energy
