If you lack one eye you’re one-eyed, and if you lack one leg you’re one-legged. It then stands to reason that if you lack one finger you’re nine-fingered.
And no, this is not any half-brained guy making it up. Chishō Takaoka (1896-1944), a geisha who chopped off one of her fingers to make some sort of point, became internationally famous as the “Nine-fingered Geisha” (Wikipedia). And Japanese yakusa gangsters that chop off one of their own fingers, presumably of the sort that haunt your izakaya, are often referred to as nine-fingered (emphasis mine in all quotes):
He employs a bodyguard who doubles as a chauffeur, an ex-yakuza who cut off his pinkie finger years ago as a gesture of apology to a gang superior. Adelstein says he needs a car and a nine-fingered driver in order to avoid the subway, where a hit man might shove him in front of a train. (Peter Hessler, “All Due Respect,” The New Yorker, Jan 9, 2012.)
Despite the folklore surrounding groups, the modern-day yakuza are entrepreneurs, rather than the tattooed, nine-fingered thugs in white suits wielding samurai swords of popular imagination; (Jake Adelstein, “Mobsters on a mission: How Japan’s mafia launched an aid effort”, Independent, 8 April 2011.)
Your example suggests the nine-fingered yakusa men. But if someone lacks more than one finger you could just adjust the number: an eight-fingered pianist, a seven-fingered shark handler. If an indeterminate number fingers are missing, perhaps single-digit-fingered?