I think the difference is that under 1/0 policy gradient loss, it gets feedback only on the actual chosen move. Under MCTS-rollouts-each-move, it gets feedback

I think the difference is that under 1/0 policy gradient loss, it gets feedback only on the actual chosen move. Under MCTS-rollouts-each-move, it gets feedback on every move on the board whether its value estimate was slightly too high or low plus the ultimate outcome of the 1 move it did make.