I'd recently read in a non-fiction work (reference lost) that there are some languages that have no generic term or category for animals, ie no equivalent of "animal." Does anyone have any information or references to chase on this?
It may be true in some Bantu languages. The word "nyama" is widely translated as "animal", but when you ask trick questions like "Is a slug a type of animal?" (in the language), people tend to say "No", unless they are well-educated (have taken a zoology class and have been taught about Animalia). If you simply ask for translations into English, you'll get "nyama" translated as "animal" but I think it is more likely to be "mammal" extended to "animal" because there is a terminological gap in the language.
Well, English has no generic term, but differentiates animal into generic / specific through syntactical means and contextual clues. English prominently treats dogs as neuter, the dog as class, etc. By which I mean animal is no grammatical class in English. The word animal is a word like any other and so fuzzy and polysemic that your question is nearly meaningless. The modern understanding of the division in eukaryotes and prokaryotes necessarily does not exist in primitive cultures.
Overthinking it a little bit, considering 6726's answer, I find that Ger. Ungeziefer or Untier (same root?), and Viech make a similar distinction as is implied above for some African language, that is a distinction to Tier "Animal", and Vieh "domestic animal"; potentially the distinction is reasonable, animable (cp perhaps Ger annehmbar?) vs uncontrolled, beasty, or monstrous creature. Also cp undead "inanimate". *pe'k-u-, whence Vieh might originally refer to horned animals or bound, cp pungo "sting" (thinking of a lasso attached to a stake driven into the ground), or caught, cp OHG fahan ...
By the way, I'm not sure Insect follows the same pattern; it's usually explained as in sections, referring to the compartmentalized bodies, the proverbial waste like a wasp.
I just looked up the word "animal" (and about 100 other words) in almost every writing system (picking the main language in that writing system) and they all have the word "animal". It is even included in the standard Swadish List, of which there is one for most languages. I would check an obscure or lesser documented language to see if that's the case. Even this has animal. So I think this author was mistaken or thinking very deeply about the meaning of the word and probably had some intuition he was referencing.