This paper proposes a novel game-theoretic decision-making algorithm for safe maneuver planning in highway driving. The problem is formulated as a two-player extensive-form game for safety between the ego vehicle and the environment (all the other vehicles around). In order to make a decision (i.e., plan maneuver), the ego vehicle builds a game tree in the current state. The tree is expanded for each possible maneuver of the ego vehicle and the observations from the environment. For evaluation, we quantify the safety value of a maneuver by computing and over-approximating its trajectory and checking for the worst-case spatiotemporal overlap with possible trajectories of other vehicles. The ego vehicle tries to maximize the safety value, assuming that others will act to minimize it. Among equally safe maneuvers, it chooses the one that travels the longest distance. The minimax solution of the game tree yields a sequence of maneuvers up to a predefined depth. The ego vehicle applies the first maneuver in a receding horizon fashion and repeats the process in constant planning cycles. For validation, we simulated highway driving scenarios and compared our minimax-based planning approach to a rule-based planner and an online look-ahead planner in terms of safety, traveled distance, and computation time. We have shown that our approach incorporates a higher safety level than the baseline planners at the cost of traveled distance and computation time.