Less power doesn't necessarily mean fewer games. According to the paper on AlphaGo Zero, they trained it on ~4.9 million games.
> Over the course of training, 4.9 million games of self-play were generated, using 1,600 simulations for each MCTS, which corresponds to approximately 0.4 s thinking time per move.
> Over the course of training, 4.9 million games of self-play were generated, using 1,600 simulations for each MCTS, which corresponds to approximately 0.4 s thinking time per move.