What is shown is a vambrace, or possibly a bracer repurposed to be more armor. A vambrace is a tube of armor, anything from metal to leather, used to protect the forearm. A bracer is intended only to protect the inside of the arm of an archer. What is shown in the image looks more like a bracer, but seems to be intended for use as armor, much like the confusion engendered by early D&D, which listed bracers as armor, confusing them with vambraces (which are properly part of a more complete set of armor).
As to why you would see this on a knife-fighter, knife-fighting is a very close form of combat, requiring you to move your hand and arm into the opponent's space to be able to do damage. Thus, against an opponent with any sort of blade, you run a high risk of getting your arm cut up, reducing your combat efficacy. It doesn't take much. They sell "cut-resistant sleeves", but a couple of YouTube personalities who research close weaponry have demonstrated that just about any thick fabric works as well. Knives don't cut with a great deal of force, just sharpness. If the vambrace is made out of a more rigid material, such as cured leather or metal, it may also help to protect against impact, since one of the advantages of swords over blunt objects is that they deliver an equivalent force over a much smaller area (even if the blade of a sword doesn't cut through thick cloth, it's still hitting with a comparable force as a club of the same weight).