Yes yes, a CPU converts a lot of the electricity it absorbs into heat. We all know that; that’s why we have such crazy cooling devices attached to the CPU now.
However you’re missing the most basic principle of electronics.
Your debate makes it sound like when electricity enters a light or motor, all of it is converted to light or kinetic energy, which is not the case. Think about a simple electric circuit: a device (any device) attached to a battery. Where does the electricity go? It doesn’t stop at the device; some of it is used to do whatever it is the device does, but the rest continues through the wire, back to the battery (hence the closed circuit).
A computer is no different. Charge carriers come in through the mains, enter the PSU, then to the CPU where they do their work, create heat in the process, then the rest comes out, back to the PSU, and back out to the mains.
Ian Boyd had a good start by pointing at a transistor, but did not follow it up with a tangible explanation of what exactly the electricity is used for (the “payoff” of the device, specifically as an analogy to the movement of a fan or light of an LED). You can do a little research into how a transistor works to really understand it, but suffice it to say that the electricity is used to physically alter the atomic arrangement of part of the transistor to allow or block electron flow. Granted its “action” is not nearly as clear or obvious as movement or light, but the energy is still used to do something (and as Ian mentioned, a bunch of heat is created when you push atoms around). I’ve seen some SEM photos of a CPU gate in action which really helps to visualize things; if I can find one, I’ll add it.