The point of view in Carl Stephenson's "Leiningen Versus the Ants" is third-person objective.
We know it is a third-person narrative because an outside narrator tells the story, as in the following passage:
Leiningen sucked placidly at a cigar about the size of a corncob and for a few seconds gazed without answering at the agitated District Commissioner. Then he took the cigar from his lips, and leaned slightly forward. With his bristling grey hair, bulky nose, and lucid eyes, he had the look of an aging and shabby eagle.
Note that Leiningen is not the one telling his own story; someone else is telling the story for him. (Another hint is that we never see the word "I" except in quoted lines.) The next question is whether or not the narrator is an interested or a disinterested (objective) storyteller.
A third-person omniscient narrator tells the story in the third-person, but he also interprets (makes judgments about) the story for the readers. In this story, the narrator does not take sides or make judgments on what happens, so this is not a story told by an omniscient narrator.
A third-person limited narrator tells the story but only from one character's perspective. In this case, Leiningen is the only major character, so it would be told strictly from his point of view, as in the following line from the story:
And now he was sure he would prove more than a match for the "irresistible" ants.
Without reading this story carefully, a reader might be fooled into thinking this story is told from a third-person limited point of view. It is Leiningen's story and the narrator has more to say about him than any other character in the narrative. Note the the following lines, however:
It is not easy for the average person to imagine that an animal, not to mention an insect, can think. But now both the European brain of Leiningen and the primitive brains of the Indians began to stir with the unpleasant foreboding that inside every single one of that deluge of insects dwelt a thought. And that thought was: Ditch or no ditch, we'll get to your flesh!
An objective narrator knows what all the characters are thinking and feeling, and this passage demonstrates that the narrator knows what Leiningen, the native Indians, and the ants are all thinking.
So, the answer to your question, as I stated above, is that the point of view in "Leiningen Versus the Ants" is third-person objective.