Suther, they may be hunting with handguns, but hopefully in an ethical manner.
When I was younger, I watched a fellow in Arizona shoot a small Mule Deer buck with a 357 magnum, loaded with factory 158 grain, half jacket, flat nose bullets.
The pistol was a lovely custom S&W, with an 8 inch, heavy barrel, cut with a dovetail to mount the LER 3X scope.
I watched this hunt very closely, as did the rancher, who owned the property. It was the first time he had allowed a handgun hunt on his property, and the only reason he did was because a well known author, writing for a prestigious magazine, begged and pleaded and maybe offered one of his "virgin" daughters for the privilege.
The hunt was going to be the basis for a magazine article, and the shooter was accompanied by a cameraman, who was constantly in the way.
The first shot was at just over 100yds, and the bullet went under the Deer's belly, too far back for a clean kill. Good thing he missed.
That Deer had a death wish, he stood there, broadside, until the shooter took a second shot. There was a "thump" sound as the bullet hit the rib cage, but low, just above the breast bone.
The Deer took off running as hard as it could, obviously terrified, but didn't leave a blood trail.
The shooter wanted to chalk it up to a "miss." The rancher had a different opinion.
We saw another buck about a half hour later, in the adjacent ravine, laying down, and soaking up sunlight.
The pistolero wanted to shoot it, but the rancher told him it wasn't going to happen until he got within 50 yards.
After a very slow, careful creep, the cameraman told him they were close enough, and the angle was good for a picture.
We were watching from the top of the ravine, a few hundred meters back.
The buck got their scent on the wind, stood up, stretched, and started to walk away. The pistolero took the shot and hit him just behind the shoulder, about 8 inches from the bottom. It was a good shot, and even though the Deer ran off, it fell down about 30 yards later, got up again, and wobbled for a few more yards before finally going down and staying down.
We sat and watched, as did the shooter and cameraman, for about ten minutes before getting closer. The Deer was dead.
The surprise was that it was the "same" Deer he had shot an hour and a half earlier.
The first bullet had hit the Deer, penetrated about two inches, and stopped on the rib, just at the base of the breast bone. The animal would have likely survived, with lots of pain involved, if it hadn't waited around.
Not all of the stories you read in those magazines tell the whole truth. In this particular case, the author/pistolero was ethical enough not to write the story.
The rancher allowed pistol hunting on his property afterwards, but only if the shooters could pass his skill tests, and if they were accompanied by a guide, who kept the shots within ethical ranges.
There's a very good reason you don't see a lot of articles written about handgun hunting for big game, other than hogs at close range.