
Structured nonlinear
Nonlinear games take players off the rails and take advantage of the interactive nature of games - players no longer have to follow a single predefined path from start to finish. In such titles, players are asked to make meaningful choices and have a sense of agency in either gameplay, storyline, or both. However, designers of structured nonlinear games still retain a level of oversight and control over the gameplay experience. They prepare for a series of possible gameplay or storytelling scenarios and prepare the solutions and endings. The final result is a carefully balanced and structured experience that gives a level of freedom to the players, increasing replayability and allowing players to play in a way they enjoy the most:

There are obvious drawbacks and challenges with nonlinear games. The alternative paths should be as fun and rewarding as the main one, as the moment you encourage certain play styles is the moment you take away the choice and force many players to play the game in the optimal (but potentially less fun) way. Your scope will also grow substantially, especially if hand-crafted stories branch in multiple directions. You'll also create a lot of potentially time-consuming content that most players will never explore, so take that into consideration if you plan to put the coolest bits of the game behind an unlikely branch.
In games such as Hitman, Thief, Deus Ex, or Dark Souls, players are presented with a great degree of freedom in the way they approach gameplay situations, but ultimately the structure follows an order that can be predicted and planned for.