I think a fairer reading of the paragraph isn't that he's claiming to have initiated work in cellular automata as a whole but that he's claiming to have been the initiator of the "burst of productivity" in the 80s.
But he does call it a new idea, directly followed by three strong words (ultimately, primary, initiator). I'm not saying the only reasonable interpretation of the sentence is that he's overstating his role. But what does make me cringe is that it can easily mislead readers who aren't familiar with the history of this specific idea, and that this confusion would have been easy to avoid.