There is nothing generic in the sentence "last man standing". It's referring to one person, who is, in this case, a man.
The argument, which at least makes sense, is that a "Chairman", even if he's male, should be a "Chairperson" because the office is not male, and therefore the title shouldn't be gendered.
That just doesn't apply here. "A Chairperson" makes sense, "a last man standing" doesn't.
"Last person standing" is also something you could say, but the title didn't, and there is no cause to 'correct' it, because it isn't wrong.
The argument, which at least makes sense, is that a "Chairman", even if he's male, should be a "Chairperson" because the office is not male, and therefore the title shouldn't be gendered.
That just doesn't apply here. "A Chairperson" makes sense, "a last man standing" doesn't.
"Last person standing" is also something you could say, but the title didn't, and there is no cause to 'correct' it, because it isn't wrong.