It seem that the textbook "Machine Learning - A Probabilistic Perspective" uses input and output in a opposite way, is it?
No, it is not the case. I’m almost sure that it’s a typo and it should be changed to:

“We now consider unsupervised learning, where we are just given input data, without any outputs.”

It can be deduced by looking at the definition of supervised learning from the book:

“In this section, we discuss classification. Here the goal is to learn a mapping from inputs x to outputs y, where y ∈ {1,...,C}, with C being the number of classes.”