BEIJING — For months, Chen Guangcheng, one of China’s best-known dissidents, played a cat-and-mouse game with the phalanx of guards encircling his home. He dug a tunnel to try to escape, a friend says, but was found out. And he sneaked out a video that alerted his supporters to the smothering confinement he said he and his wife endured at the hands of the men who kept them virtual prisoners in their rural farmhouse.