One of the fundamental challenges in 5G and beyond technologies is to support short packet transmissions while ensuring ultra-reliable and low latency  communication. Due to the distributed nature of the network, interference is almost unavoidable in most of the emerging communication scenarios. In addition to this, data arrival at the users is bursty in nature. The performance of various interference mitigation techniques for short packet communication under bursty traffic is not well understood from the existing literature. To address these issues this work considers the problem of short packet communication over two-user Rayleigh fading Z-interference channel (Z-IC) under random arrival of data at the users. The work characterizes the stability region of the 2-user Z-IC which takes account of random arrival of data at the users. The evaluation of the stability region involves determination of probability of successful decoding for the various interference mitigation techniques such as joint decoding and successive interference cancellation. The probabilities of successful decoding are characterized for various interference mitigation techniques using the framework of finite block-length information theory. The developed results take into account the packet length, rate, underlying channel model and random arrival of data at the users. The developed results also help to explore the impact of interference on average delay and average age of information for various interference mitigation techniques.