The key thing humans got is replacing the genetic evolution by memetic evolution, aka culture, powered by structured communication aka speech. This allowed for organizations above the Dunbar number, and very quick evolution of behaviors without constantly killing and re-spawning physical bodies.
Some advanced animals, like wolves, have something resembling a passing of cultural knowledge: they teach their young how to hunt particular prey, and this may differs seriously between packs and types of prey. But they lack speech, so they can't pass more complex ideas.
Cetaceans are said to have consciousness not unlike humans'; maybe they have speech and an advanced culture; we don't know. But they lack means of manipulation and live mostly floating above abyss, so they don't have a material culture and technology.
Quite possibly it's not an exceptional intellectual capability that singled out humans among comparably intelligent animals, but the (proto-)speech ability. The advances in intelligence then followed, being evolutionary beneficial.