How to define a neural model as linear or non linear
You are right, for the model to be non linear, the activation function must be non linear.

If the activation function is for example the identity function, your model won't be non linear, even if you stack multiple hidden layers. Indeed, the output of the neurons will only just be a linear composition of the inputs combined with weights.

I think the author says this neuron model is non-linear because in practice a linear activation function is almost never used. Some functions look like linear functions, but in fact these are not. Here is a demonstration for the ReLU activation function, which look like a linear function but is mathematically not : https://datascience.stackexchange.com/a/26481/73209

I guess it is the same for the Piecewise Linear Unit (PLU) activation function.