Wave propagation in ray-chaotic scenarios, characterized by exponential sensitivity to ray-launching conditions, is a topic of significant interest, with deep phenomenological implications and important applications, ranging from optical components and devices to time-reversal focusing/sensing schemes. Against a background of available results that are largely focused on the time-harmonic regime, we deal here with short-pulsed wavepacket propagation in a ray-chaotic enclosure. For this regime, we propose a rigorous analytical framework based on a short-pulsed random-plane-wave statistical representation, and check its predictions against the results from finite-difference-time-domain numerical simulations.