Recent studies in bioinspired artificial olfaction, especially those detailing the application of spike-based neuromorphic methods, have led to promising developments towards overcoming the limitations of traditional approaches, such as complexity in handling multivariate data, computational and power requirements, poor accuracy, and substantial delay for processing and classification of odors. Rank-order-based olfactory systems provide an interesting approach for detection of target gases by encoding multi-variate data generated by artificial olfactory systems into temporal signatures. However, the utilization of traditional pattern-matching methods and unpredictable shuffling of spikes in the rank-order impedes the performance of the system. In this paper, we present an SNN-based solution for the classification of rank-order spiking patterns to provide continuous recognition results in real-time. The SNN classifier is deployed on a neuromorphic hardware system that enables massively parallel and low-power processing on incoming rank-order patterns. Offline learning is used to store the reference rank-order patterns, and an inbuilt nearest neighbor classification logic is applied by the neurons to provide recognition results. The proposed system was evaluated using two different datasets including rank-order spiking data from previously established olfactory systems. The continuous classification that was achieved required a maximum of 12.82% of the total pattern frame to provide 96.5% accuracy in identifying corresponding target gases. Recognition results were obtained at a nominal processing latency of 16ms for each incoming spike. In addition to the clear advantages in terms of real-time operation and robustness to inconsistent rank-orders, the SNN classifier can also detect anomalies in rank-order patterns arising due to drift in sensing arrays.