Not one but ...

Herman Melville - The Confidence Man

http://www.online-literature.com/melville/confidence-man/10

"You would not hint that the colored cravats would be so bungling as to lose, and the dark cravats so dextrous as to cheat?Sour imaginations, my dear sir. Dismiss them. To little purpose have you read the Ode you have there. Years and experience, I trust, have not sophisticated you. A fresh and liberal construction would teach us to regard those four players-indeed, this whole cabin-full of players--as playing at games in which every player plays fair, and not a player but shall win."

Does it mean

Not only one person but all but...

Is it a negation when he says "not a player" instead of all players?