I'm not familiar with the details of backprop in neural networks, but AIUI it's an application of automatic/algorithmic differentiation, which comes in two modes: forward and reverse.

Reverse mode is harder to implement as you need to retain state through the calculation, but it scales differently. Forward mode is O(number of inputs) while reverse is O(number of outputs). Seems obvious that reverse mode is what you want for training a neural network, where you have huge numbers of inputs and usually one output, the loss you're training on.

(And indeed that appears to be what the article is saying, in different language.)