Integration of heat and electricity supply improves the overall energy efficiency and system operational flexibility. The renewable powered heat-electricity energy system is a promising way to set up residential energy supply facilities in remote areas beyond the reach of power system infrastructures. However, the volatility of wind and solar energy brings about the risk of supply inadequacy. This article proposes a data-driven robust method to quantify two measures of such a risk in the stand-alone renewable powered heat-electricity energy system. The uncertainty of renewable generation is modeled through a family of ambiguous probability distributions around an empirical one based on the Wasserstein metric; then, the probability of heat and electricity load shedding during a short period and related penalty cost are discussed. Through a polyhedral characterization of renewable power feasible region, the load shedding probability under the Wasserstein ambiguity set comes down to a linear program. With a piecewise linear optimal value function of the penalty cost, its expectation under the worst case distribution in the Wasserstein ambiguity set also gives rise to a linear program. The proposed method requires moderate information on renewable generation and makes full use of available data, whereas sustains computational tractability. The evaluation result is robust against the inaccuracy of renewable power distributions. Case studies demonstrate the effectiveness of the proposed approach.