If we define "moving" as "producing strong emotion," then I would argue that the main emotion to be evoked in this tense short story is fear. The situation in which our protagonist finds himself is tense from start to finish, and Alan Paton shows his mastery of the written word by weaving in various literary devices and techniques, including alliteration, similes, personification and suspense.
The first literary device that jumped out for me was the alliteration used to draw attention to what the criminals want, which is money. Alliteration is the repetition of consonant sounds, as in:
His wages were in his purse ... weighing heavily.
The repetition of the heavy "w" sound helps us as readers to feel the weight of the situation, and the concern we have already felt for the protagonist's safety is heightened.
Secondly, a simile, which is a comparison using "like" or "as," is used to describe how fast his heart is beating:
His heart was like a wild thing in his breast.
Thanks to this simile, we can imagine just how fast and hard his heart is pounding in his chest as these events play out. The simile makes the story moving by making the man's fear palpable.
After our protagonist has "plunged blindly into the wilderness of wire," (note that Paton once again uses alliteration on the letter "w" here) personification is used to breathe life into the trash that he finds himself immersed in. The "grotesque shape of wire" is described as tearing at him and holding him until he cries out for help. By creating a scenario in which the inanimate wire takes on human-like qualities and seems to initiate a further attack on our protagonist, Paton moves us to feel pain on behalf of the protagonist. Personification is thus the third device that Paton uses to make the story moving.
I would argue that a final technique that Paton uses to keep this story moving is suspense, which builds right from the beginning, when our protagonist gets off the bus and sees the young men waiting for him. He knows immediately that he is in trouble. All the actions that follow, until he is lying under the lorry and realizes that his son is dead, build on the suspense created right in the beginning. Thanks to the suspense, a reader is unlikely to stop reading this short story once they have started.