Boxy Bennett is Gotham's resident mobster, who has his sticky fingers in every dirty deal in Gotham. Born into a family of crime, he decided not to break out, and stay in the family business, which was providing very nicely for him. Boxy Benett is a middle tier mobster and owns a few rackets in Gotham City, including secret gambling operations. He also owns a legal business of a fish market, which is arguably a front for his illegal businesses. Bennett has thus run up against some of Gotham's most notable criminals, such as Harley Quinn and The Joker. Boxy has,in fact,an attraction to Harley Quinn. This attraction often led him in direct conflict with Batman and the police.
While he may not have criminal empires to match Rupert Thorne or the reformed Arnold Stromwell, Boxy does have his gang. In fact, Bennett was bold enough to encroach on the Joker's territory, taking advantage of a prolonged absence to the Clown Prince of Crime to seize the Apex Theatre, which was one of the Joker's establishments, and use it as a front for a numbers racket. His racket is the same as any gangster thug, racketeering, protection, embezzlement, and blackmail to name a few. He ended up arrested finally by Detective Harvey Bullock.
Later, Boxy makes a cameo appearance in Batman Gotham Adventures #11, during which he is tortured by The Riddler for information on some of Gotham's most wanted, so The Riddler could leave clues for Batman to catch them, one by one. After being in constant agony, via The Riddler's cane and it's weaponry, Boxy gave in.
Boxy made his last DCAU appearance in Batman Adventures. Firefly torches Boxy's illegal gambling sites when he refuses to pay The False Face Society extortion money. As a furious Boxy shouted at the arsonist, Matches Malone knocked him cold at Firefly's order.