It might have been Nolan's idea, but the first Chuck E. Cheese was actually created, operated, and owned by Atari. Nolan wanted Atari to have a place to operate and profit from the arcade machines they built. But the engineering work, marketing etc. was all done by Atari employees.

When Warner Communications bought Atari from Nolan, they really didn't want the restaurant. So Nolan bought it from them, took it private, and expanded it.