Injecting alternative gas (e.g., green hydrogen from wind generation) into the gas system is a promising way to decarbonize the energy sector. However, the fluctuating renewable generation could lead to time-varying alternative gas injections. Then, the gas composition in the gas system may become uncertain, increasing the short-term risk of the integrated power-gas systems during the operation. This article proposes a short-term reliability assessment approach for IPGS with alternative gas injections. First, the multi-performance and multi-state universal generating functions (UGF) are constructed to efficiently model the short-term reliability of the power-to-gas facility and the wind farm, respectively. Then, a reliability management UGF operator is proposed to minimize both load shedding and gas security violation. A set of novel reliability indices is proposed to comprehensively assess the gas security violations under uncertain gas compositions. Moreover, an analytical short-term reliability assessment approach is proposed, where the state-based sequential approximation and state-based McCormick envelope techniques are tailored and embedded. By optimizing the solution order by the system states, the nonconvexities in the reliability management optimization problem can be handled tractably without increasing the computation burden. Finally, the IEEE 24 bus Reliability Test System and the Belgium gas system are used to validate the proposed approach.