For decades, Chinatown Fair welcomed everyone — misfits, cool kids, world champions, novices, dancers, fighters, strategists, tourists carrying leftover dumplings from their dinner across the street. Then, two weeks ago, it disappeared. Even among the devoted gamers and urban nostalgists who had been whispering about its demise for weeks, the end came as a surprise. About midnight, a simmering rent dispute forced Chinatown Fair, a video-game arcade at 8 Mott Street for several decades, to shut its doors; by the next evening it was stripped bare, an empty shell of a retail space with an old battered sign.The place had always been hard to pin down. How did a dingy spot like that hang on so long? How did it have access to the newest Japanese games, long before they appeared elsewhere in the United States? And how did the live chicken that for years stood near the entrance learn to play such a mean game of tic-tac-toe? But nothing about Chinatown Fair was more mysterious than the speed with which it vanished, giving rise to a thousand theories about what had befallen the arcade and what would become of the community it used to house.