How many ways can a company select 4 candidates to interview from a short list of 12 engineers?

As asked, the question is seeking to know the number of subsets of size 4 in a set of size 12. A subsequent accounting for the order in which they are chosen is a change in the nature of the question. So there are $${12\choose 4}$$ ways to do this. Your interpretation is correct.

Were order important, you would be asked the number of ordered subsets of size four, or you might be asked to name them something like president, vice-president, secretary and treasurer. This labeling can be done to each subset of size 4 freely, so it boosts the count by a factor of $4! = 24.$ No such secondary labeling is present in the question.

Being asked to choose "a group (set) of size 4" implies sampling without replacement.

In a word, the book is on rock-solid ground.