This paper studies a robust asset-liability management game between two strategically interacting fund managers with relative performance concerns measured in terms of their funding ratios. The managers have specialized investment opportunities in a market with stochastic volatility and face heterogeneous liability commitments subject to idiosyncratic risks, while their investment decisions endogenously affect risky-asset expected returns through both own-market and cross-market price impact. Each manager seeks a robust investment strategy that maximizes the expected CRRA utility of her terminal funding ratio relative to that of her competitor under the worst-case probability measure. We derive semi-closed-form robust Nash equilibrium investment strategies and characterize the associated worst-case model distortions through a coupled Riccati system. A verification theorem establishes the admissibility and optimality of the equilibrium controls. Our analysis shows that relative performance concerns and price impact affect worst-case model distortions in two distinct ways. Relative performance concerns make competitor-specific shocks relevant to each manager’s robust evaluation, whereas price impact affects the worst-case distortions indirectly by changing equilibrium investment positions and the associated risk exposures. Moreover, stronger relative performance concerns do not necessarily induce herding-like behavior: they may either reinforce or weaken strategic substitution, depending on the interplay among cross-market price impact, ambiguity attitudes, and common risk exposures. Strategic complementarity arises only when relative performance incentives are sufficiently strong to outweigh the adverse effect of cross-market price pressure. Numerical experiments illustrate how relative performance concerns, ambiguity aversion, price impact, and heterogeneous liability exposures shape the equilibrium investment strategies.