The answer depends on your interpretation of "civilized". General Zaroff takes great pride in being civilized on the remote and desolate Ship-Trap Island. His palatial chateau boasts the finest ammenities from around the world. While Rainsford is in his company, he enjoys delicious food and wine, the finest clothing, and most expensive bedding. However, General Zaroff believes that his education and posh lifestyle make him superior. The sailors he hunts and kills are less civilized than he is, and therefore, he should be allowed to take their lives. After all, sailors won't be missed for they are thieves and outlaws. Perhaps Richard Connell is making a statement about mankind in general. Most people consider themselves civilized, yet their action, or inaction, proves them to be less than civilized.
This is a central question that the text demands us to ask ourselves. The character of Zaroff seems to be deliberately problematic in the way that he has every appearance of being highly civilised and sophisticated, yet at the same time holds such abominable views that allow him to justify murder in his own mind. From his first introduction, Zaroff is said to speak in a "cultivated voice." He has created a setting that has all the amenities of civilisation, in spite of its remote location, as the following description makes clear:
The dining room to which Ivan conducted him was in many ways remarkable. There was a medieval magnificence about it; it suggested a baronial hall of feudal times, with its oaken panels, its high ceiling, its vast refectory table where two-score men could sit down to eat.
Thus, in his accent, appearance, setting and the way in which he is able to engage Rainsford in intelligent conversation, Zaroff is most definitely civilised. However, in one crucial area, he most definitely is not. His own philosophy of the world, that argues "life is for the strong, to be lived by the strong, and if need be, taken by the strong" presents him as a cold-blooded killer. I am reminded of Nazi Generals who had a real appreciation for the arts yet at the same time killed thousands of Jews in terrifying ways. Therefore, above all, although Zaroff is civilised in his appearance and character, his attitude clearly presents him as uncivilised.