They didn't have any writing. The quipu were basically accounting, using numbers and keys. The corded strings have actually been partially decoded. None of it contains enough information to build a structure. This kind of thing could have evolved into actual writing, as it did in China and Mesopotamia. In each case, writing was preceded by marks on bones or clay, before it actually developed into writing. It's notable that the Chinese heated turtle plastrons and read the cracks that developed as a way of divining answers to questions. Supposedly, the character "not" 不 is derived from the crack so interpreted on the plaston.
Such systems emerged from earlier traditions of symbol systems in the early Neolithic, as early as the 7th millennium BC in China and southeastern Europe. They used ideographic or early mnemonic symbols or both to represent a limited number of concepts, in contrast to true writing systems, which record the language of the writer.
And the methods the Inca used, was borrowed from an earlier culture, the Tiwanaku, which didn't even use quipu.
Tiwanaku (Spanish: Tiahuanaco or Tiahuanacu) is a Pre-Columbian archaeological site in western Bolivia, near Lake Titicaca, about 70 kilometers from La Paz, and it is one of the largest sites in South America. Surface remains currently cover around 4 square kilometers and include decorated ceramics, monumental structures, and megalithic blocks. It has been conservatively estimated that the site was inhabited by 10,000 to 20,000 people in AD 800.
This doesn't mean the Inca were smarter than many Old World cultures. As you know, Jericho, Stonehenge, and Gobekli Tepe were also built by preliterate peoples.