Quoted from TopMoose:
It's a dopamine rush - your brain is rewarding you the same way it does when you get a Facebook notification, hear a great song or taste your favorite food. With pinball, you're getting chemical rewards whenever you complete an achievement, beat a timer or get it to make a certain sound or display a special light show or animation. Dopamine can be addictive.
To build on this, I’ve often reflected how pinball relies on certain mental abilities that were very important in our evolutionary past, but not so much in the modern world. Namely, mental geometry in calculating angles and using precise timing to hit targets, catch something, or prevent something from escaping. Think how close this resembles skills needed to hunt (hit a moving target by chucking a rock) or more advanced methods like bow and arrow or later guns. Or Spearing a fish in a stream. Or brains reward us for exercising skills important to our survival. So our brains like it when we play pinball. This is only one dimension of the answer and many others responses only build on this.