In the framework presented C. Thi Nguyen in his book Games: Agency as Art, striving play is a mode of game-playing in which we play for the sake of striving. We try to win the game, but whether or not we win is ultimately irrelevant; we’re ultimately motivated by either the experience of striving in itself (intrinsic striving play) or something that results from that striving (instrumental striving play)—like the fitness that comes from playing tennis.
Nguyen points out that striving play involves a “motivational inversion”, in that we temporarily adopt the game goal as a way to achieve our real goal, which is the striving itself. In striving play, we “pursue the ends for the sake of the means”. Contrast with achievement play.
Nguyen, C. Thi. Games: Agency as Art (pp. 8-9). Oxford University Press. Kindle Edition.