The term, taken of course from chess, refers to how we, as human beings, can use our free will (if it is not an illusion) to go out of this bodily existence, to cease to exist. Just as in chess, or any action requiring decisions, we are called upon to choose a “strategy,” for example, aggressive resistance, or gradual attrition, or graceful moves to avoid the final annihilation, etc. Beckett places his characters in a closed setting, like men on a chessboard (without a superficial one-on-one relationship), to imitate not the act of ending, but the condition of each of us as we approach the end of our own facticity. Your idea of “a game of ends” is rather insightful, but the connotation of “game” implies not only a frivolity, an inconsequentiality, to its outcome, but also assumes that there are hard and fast “rules,” both notions that Beckett would reject. A better interpretation would be that Beckett had found a way to state everyone’s situation–we are near the end of our choices, and we must choose a strategy for our “endgame.” Those of us who have made bad choices in the "middle game" have fewer options.