Typically, a marker interface is an interface that alone by its presence has some sort of effect. In other words: some sort of framework will use instanceof
or maybe reflection to identify situations where some object or class implements that marker interface, to then do something based on that information.
And I agree to your understanding: calling a specific method of that interface isn't part of that concept "marker interface", at least in my book.
And beyond my book, that seems to be a well known convention: marker interfaces do not declare a method, see here or there. Both these sources emphasize: a marker interface doesn't have methods or constants.
Therefore I agree with your stance: Function and other interfaces in that package aren't marker interfaces in that strict sense.
On the other hand, I doubt that you will find an "official" definition of that term (for example in the Java Language spec). And when there is no official standard, people are free to make up the "meaning" of words.
So maybe your interviewer decided that "being a SAM" interface is somehow a "marker", too. And I am pretty sure you can't sue him for his opinion.