Computer engineering is the hardware level of designing and building computers, it might involve firmware depending on the job and the area but it’s way closer to electrical engineering than software engineering. Software engineering is also very different than computer science.
Software engineering is called that because it is the equivalent of engineering in software. You are engineering and designing a product/system. Computer science is more of the theoretical side, more detailed study of algorithms and math, etc.
What do you think of electrical engineers? Is that “real” enough to be called engineering?