The Engine did influence computing, just not in the manner you and too many others like to believe it did.
Computing as "you know it" requires both hardware and software. Because current computing is primarily electronic in nature and the Engine was primarily mechanical in nature, the Engine did nothing to influence computing hardware.
But what it could have done is prompt research in that area. Had the Difference Engine been successful, the Analytical Engine could relatively easily have followed, which would have been, in effect, a mechanical computer, and a mechanical computer is still a computer.