When I say "tough mobster" I mean a guy who would operate a club that is a total front. I don't mean a physical presence, I mean a characterization. Or, more to the point, I mean the way in which someone who would run a criminal operation through a nightclub would be in real life. I consider such a person to be a mobster that would have to be willing to order the dirty work to be performed. Such a person I consider to be "tough" and their profession is a mobster. Hence the term "tough mobster." In the comics, Penguin can talk a pretty big game and doesn't back down from his criminal brethren. Again, I consider that "tough," even if he does at times play both sides and eat them out to the cops or Batman if it suits his needs.
And I've never played an Arkham game.