David Dodge, acting president of the American University of Beirut, was released by his kidnappers after a year of captivity, the White House was told. Presidential spokesman Larry Speakes said Mr. Dodge is described as in ''excellent physical and mental condition.'' Dodge was kidnaped by two gunmen in west Beirut while en route from his office to his campus residence. The White House provided no information on his treatment during captivity, the circumstances of his release, or the identity of his captors.