It’s not about there being “a thing” that makes humans unique, though. It’s about all the things combined — the emergent property of the interaction of those set of things. And it’s about degree — having an opposable thumb is not the same thing as using it in fine tool use. Passing on a particular ritual is not the same thing as developing a set of complex social norms. Hunting in packs us not the same thing as both having distinct roles and also having the concept of the others’ roles, such that you can understand the top-down system and perform role-reversal as necessary. Being able to communicate that a predator is here is not the same thing as using language to plan an activity in advance. If your chain of reasoning leads you to conclude that humans are not cognitively unique as a species, I’d suggest that you take a look at the outcome of human endeavour and then try to work out what you’re missing, rather than just conclude that humans are actually, logically, the same as a frog or an elephant.
Language, by the way, is an example of something that needs collaborative interaction, not just triadic interaction. Language in the full, rich, cultural tool sense of that idea. To converse, you have to know that the other person knows that you know something. You have to have the joint intention to make sense of that thing. You have to play roles as part of making sense of it. You need to switch between those roles, which requires understanding the concept of conversation. Animals can learn a lot of words. They can learn to respond to commands. They can learn to sign or articulate particular words. But we’ve never been able to reach them to converse, they can’t use the planning function of language. They can’t articulate abstract ideas about the future. There is a limit beyond which they can’t go, because they don’t have dialogic representation.