There were a lot of ancient societies that didn't have money but still engaged in commerce. The ancient Egyptians payed taxes in food for example. What the article stresses is that we don't have a record of the Incas' merchant class. This doesn't mean they didn't have one; they had no writing system either so it's possible that Inca trade was simply never recorded.

One thing to remember about the Inca's though is that though they had no written language, they did have a record keeping system involving knots in string. Only a very few Incas knew how this system worked so it's possible that here was no efficient reckoning system available to the masses so large scale trade would have been impossible in a lot of ways.

Another thing to think of, is that when talking about the 'Incas' we should avoid conflating the Incas themselves, who were relatively few in number, and the vast number of peoples that they ruled over. The bulk of the Incas themselves were soldiers in the military and were provided for directly by the government, while the conquered peoples were reputedly pressed into labor and made to wear uniforms corresponding to their social statuses. It's possible that the various tribes traded amongst themselves before they were conquered by the Incas and had their societies radically transformed.