The plot you are referring to is not the function produced by the neural network! It is the plot of real target variables vs predicted target variables. The straight line $y=x$ represents a perfect model.
It certainly is true that a neural network might produce a linear function in the end, but that doesn't happen in this case (as you should expect from the bivariate plots earlier on in the notebook).
For example, add the following to a new cell to view the model's output vs Weight (taking a 2D slice by setting the other variables to medians/modes):
slice_data = normed_test_data
for col in ['Cylinders', 'USA', 'Europe', 'Japan', 'Model Year']:
slice_data[col] = slice_data[col].mode().iloc
for col in ['Displacement', 'Horsepower', 'Acceleration']:
slice_data[col] = slice_data[col].median()
slice_pred = model.predict(slice_data).flatten()
A copy of the notebook with that added