There's a lot going on with the word 他｛ひと｝ here.
First, the assigning of the reading of ひと(人) to 他 (or substitution of the kanji 他 for 人) is an instance of a creative author exercising his literary license.
Second, here, as he sometimes does elsewhere in the book, the Cat is (despite his titular/opening declaration) describing himself as 人
(person). This is not so much because this sapient feline identifies himself as a homo sapience as because the word is being used loosely, to mean not a human being but any individual being possessing person-ness, which he is.
Third, I think this 人 can said to be an indefinite noun phrase (though the Japanese lacks such marking here) having a specific and identifiable referent.
Plus, this is also a case of referring to oneself in the third person. But with the word 人 it's a common practice, to which fact the presence of the eighth definition of 人 in this dictionary attests:
So the quote may be more literally rendered: "Even when a person/man is shivering on the wooden floor of the kitchen, heartlessly she remains indifferent," where it is clear by convention and from the context that by "a person/man" the Cat himself is referred to. Hence their decision to translate the 他｛ひと｝ as "I"