Conway's Game of Life: Is it really P-complete?
Your misunderstanding is the meaning of parallelize.
In this context, an algorithm can be parallelized if using polynomially many processors, you can compute the answer (in this case, the value of some cell) in polylogarithmic time.
Simulating the Game of Life naively takes time proportional to the number of steps. P-completeness of the Game of Life means that you cannot improve this to time polylogarithmic in the number of steps (unless $\mathsf{P}=\mathsf{NC}$).