The main reason AlphaGo Zero learns so much faster than its predecessors is because it uses temporal-difference learning.[1] This effectively removes a huge amount of the value network's state space for the learning algorithm to search through, since it bakes in the assumption that a move's value ought to equal that of the best available move in the following board position, which is exactly what you'd expect for a game like Go.
A secondary reason for AlphaGo Zero's performance is that it combines both value and policy networks into a single network, since it's redundant to have two networks for move selection.
These are the two biggest distinguishing characteristics of AlphaGo Zero compared to previous AlphaGos, and the OP doesn't discuss either of them.
[1] https://en.wikipedia.org/wiki/Temporal_difference_learning