Yes, it is a classical NN with a single output node. I'm not disputing that, I just think their calculation of depth is strange. The network only applies the sigmoid function twice, and would ordinarily be regarded as having a depth of two. The third linear layer is fixed to multiplying by 1, which is what I meant by "has no effect". (Did you miss that I was talking about the third layer?)
Here's a diagram [1] of a one-hidden-layer NN. It has 2 activation functions. Their NN is of the same type.