The English title consciously evokes the game of chess, a favorite game of Beckett's and a recurrent element in his work. One definition:
endgame -- Chess. the final stage of a game, usually following the exchange of queens and the serious reduction of forces. (Random House Compact Unabridged Dictionary)would seem to be an apt description of the desolate setting of this play.
To push the analogy further: Hamm would be the King, the most important piece on the board, but with limited power of movement; Clov has been likened to the Knight, with his comparatively great (but idiosyncratic) mobility; Nagg and Nell, the most restricted and ineffectual "pieces," would appear to be Pawns.
By the end of the play, Hamm has bid farewell to his Knight and and his Pawns no longer respond. Perhaps he is approaching checkmate (a pharse derived from the Persian, shah mat, "the king is dead"), though in chess, interestingly, the King can never actually be taken.
Chess also figures as a trope for Beckett's work as a whole. In the words of Hugh Kenner:
...similarities must be noted with caution, lest we place ourselves in the position of supposing that having seen one chess game -- rooks, kings, bishops, pawns -- we have seen them all. Each Beckett project starts afresh a new work, a new kind of work, a new kind of experience. There is always attrition, as there always is in chess. there is always a mate, or the nearing threat of a mate. But no two games are the same. (A Readers Guide to Samuel Beckett)