Montresor does not actually directly kill Fortunato. What I mean by that is that Montresor does not do something like strangling or stabbing or shooting him. What Montresor actually does may be worse than that. He gets Fortunato down into his wine cellar and then he chains him to the wall. When he is chained, he builds a brick wall around him. Now, Fortunato is down there and can't get out. He will, presumably, die of lack of water in a few days.
So, you can answer it in a coupleof ways, I guess -- he kills him by walling him up or he kills him by not giving him water. One of those would be how I'd answer that.