By “winning the world”, Lao Tzu is talking about spiritual attainment, seeing that you and the world are not separate. It’s this insight that “gets done” by letting it all go. The “letting go” is the relinquishing of all ideas of subject and object, and with them the seeming solidity of both the objective world of phenomena and the subject who experiences that world. Both the objective world and the experiencing subject disappear when this “gets done”.
But this non-duality has always been the case, even before we realize the truth of it. It has always been right out there in the open, free for the seeing. This is why striving for it is useless. To “try and try” is to assume that the truth lies beyond one’s grasp, or is not immediately evident. This assumption causes us to overlook the truth in all its open simplicity. Instead, the world is won by simply letting go of our idea that we are separate from it.