"The Last Leaf" by O. Henry utilizes the technique of personification to present an illness as a character. Pneumonia is indeed a character that battles and defeats many of the citizens. Mr. Pneumonia is perhaps created because O. Henry's style was to write about the forces that plagued the commoner:
The author is obviously the friend of the “little man” and the enemy of those who would exploit him (Enotes).
In keeping, this Mr. Pneumonia is not presented as a "chivalric" (O Henry) opponent. Nor is he a beast with fangs or brilliant evil genius. Instead, O. Henry presents him as "the red-fisted, short-breathed old duffer." The description is appropriate both for physical and personality reasons.
Pneumonia is a disease in which the lungs begin to fill with fluid, making breathing harder and harder. Thus, the description points to this physical symptom of the ailment. Also, the description of the red skin and older age of Mr. Pneumonia suggests that this character is one who could be approaching death himself and prone to outbursts of anger. He could be jealous of the life in others and want to pull them into the metaphorical grave with him.