@Athengrim
It's actually horrifying to me that you took the "races" part and not the "human" part.
Different nationalities of humans aren't REALLY "different races". It was a method for putting down OTHER "races" to make one race seem superior. Calling white people the "human race" and black people "the other race" was a way to dehumanize people.
Like you said, take the whole phrase. Human Race. Replace the first word with an alien species. The Asari Race. Or just look up the actual proper, original defintion of race.
Humans are all members of the human race. Our differences stem from history, nationality, culture. Not because we are physically distinct beings.
The Elven Race is a race of elves. The Dwarven Race is a race of dwarves. Not a race of human dwarves, or human elves.
Edit: This is probably easier to understand from old RPG's and stories, like maybe D&D or lord of the rings. Orcs/Orks are VERY CLEARLY not human. Warhammer orks are essentially intelligent fungus. THESE are distinct races. Elves and Dwarves blur the line because it's easier for us to overlap "human" onto something that just has different ears or their women have beards. It was simply easier. Even in science fiction it was cheaper to make aliens look human with green skin (Star trek) on the set than it was to actually have to produce some kind of alien looking creature. The first CGI aliens were just godawful.
Biologically at least, WAY more than what you realize is actually going into really creepy territory. Kirk was not sleeping with dozens of somehow human alien races. He was literally sleeping with species that were completely biologically distinct. It's no different than a human sleeping with a tree, or a dolphin. You and I can agree it sounds pretty skeevy, but functionally it's ALL skeevy. Just depends on how far you're willing to bend your idea of what makes someone a person, or for some people, how far you're willing to bend the idea of being human.
Personally, I think the whole Tama/Elf girl thing is done on purpose to provide a different perspective on something that people don't really think about. If you swapped tama out with a generic male protagonist and replaced the girls with your stereotypical harem races, no one would have said word otherwise. Making Tama the cat, and making it REALLY uncomfortable when the elf gets really weird is kinda the point. It's a juxtaposition of our expectations.
Sorry if this was way more than you had any interest in reading, Athengrim. It's interesting to me when I get to meet someone with a different perspective.
@assman162 Wonderful name sir. By the way, one little problem... this isn't an isekai.