Here's a present (gift):
It is his dubious distinction to have proved what nobody would think of denying, that Romero at the age of sixty-four writes with all the characteristics of ____.
a dubious distinction= something that makes you noticeable that is not something that is necessarily a good or positive thing.
to prove something no one would think of denying = I can prove to you I am honest and no one I know would think of denying that, for example. That should help you understand that phrase.
the mention of age (64) is what limits this to maturity here. There would not be any reason to say the age unless something age-related was involved. It describes a point reached at an age. That is the logic used in GRE questions. Only choose the most logical idea based on the actual words and not all possible combinations.
Romero may have all the other characteristics as well but the one being stressed is maturity. None of the other words are related to characteristics related to age.
The others are wrong because:
fiction = you cannot write with the "characteristics of fiction"; you either write fiction or you don't.
inventiveness = this is a state or condition, one writes inventively or with inventiveness but not with its "characteristics"
art = characteristics of art is weird here. Again, one would probably say: writes artfully or something like that.
brilliance = the sentence would have said: writes brilliantly, if that had been what it meant. One doesn't write "with the characteristics of brilliance"
So due to the age thing and the word characteristics, maturity is the best choice, as maturity and immaturity have definite characteristics.