> It seems like the lesson we keep learning, no matter the proxy we use for intelligence, is that there is nothing that fundamentally sets humans apart from other animals

Except it doesn't show that.

The reason people make this judgement is because they don't have a coherent or clear definition of "intelligence". Nothing has been undermined, except in those who took the view that animals are dumb automatons. That's more of a legacy of modernism and the desire to gain "mastery over nature" more than anything else.

The essential feature of human beings - from which the rest of human nature and its consequences follow, including our social nature - is rationality. This entails an intellect, which is the abstracting faculty. It is the intellect that makes language possible, because without the capacity to abstract from particulars, we could not have universal concepts and thus no predicates. Language would be reduced to the kind we see in other animals.

For clarity, the functions of language are:

1. expressive: expressing an internal state or emotion (e.g., a cry of pain)

2. signaling: use of expressive to cause a reaction in others (e.g., danger signals)

3. descriptive: beyond immediate sensation; describes states of affairs, allowing for true or false statements

4. argumentative: allows critical analysis, inference, and rational justification

Without abstraction, (3) and (4) are impossible. But all animal activity we have observed requires no appeal to (3) and (4). Non-human animals perceive objects and can manipulate them, even in very clever ways, but they do not have concepts (which are expressed as general names).

Could there be other rational animals in the universe? Sure. But we haven't met any. And from an ontological POV (as opposed to a phylogenetic taxonomic classification), they would be human, as the ontological definition of "human being" - "rational animal" - would apply them.