I feel bad challenging this assumption, but I believe it is just a case of needing someone connected to the penis in a passive voice headline and they went the generic approach. Nothing special about the man, so just man. Not a male / man penis. It’s possessive.
That always takes the fun out of games for me. You can do whatever, but there’s a correct way of following the story, which is subconsciously grasped by the community and thrown down your throat if you deviate and complain you are having issues.