Whether or not the version of the story that Van der Vyver tells is accurate—and we have hints that it is not—Gordimer's story critiques apartheid.
Gordimer does this by telling the story through the white Van der Vyver's eyes. He is completely oblivious to many elements of his racism and sees nothing wrong with the racism he is conscious of.
Van der Vyver, for example, doesn't name any of the Black people in the story, except Lucas, the Black man he kills, but not his mother, wife, or child. He does, however, carefully note the names of the white people he mentions. Because of his personal friendship with the police chief, his version of what happened to Lucas—an accident—is accepted without any further investigation and enters the official record.
Van der Vyver also shows through his narrative the contempt with which he treats Black people. He insists that Lucas is his "friend," though he makes clear that he doesn't invite him into his house or go to church with as he would a white person. He thinks sneeringly about the Black people attending Lucas's funeral that they don't protect their children from "fear and pain" the way white people do. He also mentions they put aside money they can ill afford, given how badly they are paid, for a burial society, but doesn't seem to realize that he is responsible for their poor pay or seem to understand that the Black people realize they might die young and make preparations. He notes contemptuously that Black women start having babies early, in their teens.
At the end, he expects people to feel sympathy for him because Lucas is his son, not realizing he just admitted Lucas was almost certainly a product of his raping a teenaged Black employee dependent on him for survival.
Van der Vyver also takes the stance of the innocent victim, thinking it unfair that this killing will be used, as he sees it, to promote the anti-apartheid cause. He doesn't realize at all that the protesters are fully justified in using it.
Through his account, Van der Vyver shows he is a racist, a rapist, possibly a murderer (if, in fact, he wanted to get "rid" of a reminder of his rape), an exploiter, and a whiner, all of which Gordimer critiques.