It says right there in the story that Mr. Parsons is blind. It is the last line of the story "So am I."
The basic plot of the story is that Parsons is leaving his office building when a man comes up to ask him for money. The beggar is a blind man. The beggar (his name is Markwardt) tries to get Parsons' sympathy by telling the story of how he became blind.
In his story, he blames a coworker for climbing over him in the rush to escape the accident that blinded him. It is at this point that Parsons protests -- he was the coworker and Markwardt climbed over him. Now they are both blind.