The plague turns into pneumonic plague as it migrates into the lungs and causes pneumonia and a host of other respiratory problems. The causative organism of plague is the bacteria Yersinia pestis, and it is transmitted primarily by vectors (in this case fleas) from infected rodents to human beings. That is the normal route of transmission for the bubonic plague, also known as the Black Death during the Middle Ages, where 1/3 of the population of Europe died.
The thing with this "offshoot" of the plague is that it can be transmitted just by sneezing on someone. Airborne transmission is occurring, where droplets from the infected individual's coughs, sneezes, and mucous fluids carry the bacteria and spread it. If a person sneezes on the wall, and later another person touches that wall with their hand? Such contact can transmit this pneumonic plague.