Romance
This book is a romance from start to finish, even if it's not your Harlequin-branded bodice-ripper (and not just because it's hard to rip a bodice when you have arthritic fingers). From the beginning, the Major and Mrs. Ali have a chance meeting, even if it is, in essence, a very depressing one. The Major, reeling from the death of his brother, almost passes out when Mrs. Ali comes to the door. It's quite the role reversal, too, with the man feeling faint and the woman swooping in to save him.
The Major gets to do some swooping in of his own at the end. We like to define the genre of "romance" using the very technical term "chivalric stuff," and the Major is nothing if not chivalrous. When he swoops in to save Mrs. Ali at the end, he envisions himself as "Don Quixote or Sir Galahad" (21.1). You don't get much more chivalrous, heroic, and romantic than that.