If an interviewer decides not to plan any questions in advance and directs the interview in whatever direction seems appropriate at the time, what kind of interview is he or she conducting?

Unstructured interview.

Explanation:

Unstructured interview is an conversation between parts without an structured down-written questions or sequence. This type of interview is used to have an open conversation and evaluate, somehow, the skills that the interviewed could show.

So, with unstructured interviews you should be open to response different kinds of questions, personal and professional ones.