> Wikipedia says it's essentially a pure subset of Prolog, but Prolog is not classified as a functional language

That statement used “pure” in the sense of “functionally pure” (I'm not sure about “subset”; it certainly lacks some prolog features that are impure, but seems to have features that Prolog lacks; it seems more like it contains a pure subset of Prolog than that it is one.)

> I assume there must be some significant language features that e.g. functions.

I think you missed something I. that sentence, but, yes, Mercury has first-class and higher-order functions.