The results of chemical engineering show up in the materials you use, from coke bottles to fertilizer. The results of Mechanical engineering can be seen in the turning of the wheels of a car. And the results of Computer Engineering and Software Engineering are what you are looking at right now, but not the computer itself. The computer is primarily the domain of the Electrical Engineer. The computer is considered hardware and that is precisely the main concern of Electrical Engineering.
Electrical engineers use and interact with the computer to a very extensive extent.
But programming is primarily an activity in order to get something to function, to get equipment to perform some desired task, such as in programming a microprocessors and microcontrollers. In designing things, the electrical engineer may do huge amounts of computer simulations and computer modeling, but as a user of computer software written by computer or software engineers. The electrical engineer will and should be able to program to some degree because small companies may not have computer engineers on staff and the electrical engineer must be able to fill the programming function. There is a significant amount of overlap of activity between the different disciplines of engineering. As an example, take the manipulating arm of a robotic device.