Low Power Wide Area Networks (LPWAN) offer a promising wireless communications technology for Internet of Things (IoT) applications. Among various existing LPWAN technologies, Long-Range WAN (LoRaWAN) consumes minimal power and provides virtual channels for communication through spreading factors. However, LoRaWAN suffers from the interference problem among nodes connected to a gateway that uses the same spreading factor. Such interference increases data communication time, thus reducing data freshness and suitability of LoRaWAN for delay-sensitive applications. To minimize the interference problem, an optimal allocation of the spreading factor is requisite for determining the time duration of data transmission. This paper proposes a game-theoretic approach to estimate the time duration of using a spreading factor that ensures on-time data delivery with maximum network utilization. We incorporate the Age of Information (AoI) metric to capture the freshness of information as demanded by the applications. Our proposed approach is validated through simulation experiments, and its applicability is demonstrated for a crop protection system that ensures real-time monitoring and intrusion control of animals in an agricultural field. The simulation and prototype results demonstrate the impact of the number of nodes, AoI metric, and game-theoretic parameters on the performance of the IoT network.