It was a cable stayed bridge. The bridge span was just put up. The tower and the cables were to be installed over the next few weeks. They allowed traffic under an incomplete bridge because money.
Adding the tower or cables would have done nothing to strengthen the bridge. The engineers in the article suggest that the second shorter section of the bridge to be built afterwards may have alleviated some of the stresses on the north truss beam, but the truss itself was unorthodox, so they cannot say anything for certain.
The worst case would be a marching parade, on just one side, during a hurricane.
Technical description of the bridge from the engineering firm:
https://facilities.fiu.edu/projects/BT_904/MCM_FIGG_Proposal...
Page 3: "The stay cable pipes increase stiffness for pedestrian loads."
Page 18: "The stays and pylon provide the required structural design to meet the pedestrian loads for harmonic conditions of natural frequencies"
Page 64: "HORIZONTAL FREQUENCY In the lateral direction, the fundamental frequency of the pedestrian bridge shall be greater than 1.3 hertz. VERTICAL FREQUENCY The fundamental frequency in a vertical mode shall be greater than 3.0 hertz to avoid the first harmonic."
Page 65: "The pylon stiffness was designed to provide significant benefit to the overall stiffness of the structure."
The bridge that they built did not use the stays as structural elements, and any vibration dampening would have been minimal, i.e., a side-effect of stiffening the bridge rather than the reason for including them.
Unless you can find such a document: the stays were structural elements.