Understanding quantum computing through drunken walks

The problem with the article is that it never explain the main difference between classical and quantum walks.

In a classical walk, in each coin toss the probability is split.

In a quantum walk, you split the amplitude, and the value can have a sign (actually a complex phase). And you get at the end the probabilities calculating the squares of the amplitudes.

It's not clear at all how they are calculating the signs. Assuming the fang-like result of the quantum walk is not totally made up, my guess is that the yellow nodes change the sign of the amplitude, but this is not clear at all, and different setup cause different results.