We study a two-newsvendor competition problem in which both newsvendors are loss-averse and have adaptive quantity-oriented reference points. Each newsvendor faces stochastic demand determined by some demand reallocation rule and aims to choose an optimal inventory level to maximize her expected utility. Since the demand reallocation rule indicates that one newsvendor's demand affects the inventory level of the other newsvendor, this problem can be formulated as a two-person game. We prove that this competitive newsvendor problem exhibits a unique symmetric Nash equilibrium. We also show that the optimal inventory level decreases in the loss aversion degree and reference level, and increases in the competition intensity. Unlike conventional findings in the integrated risk-neutral supply chain, we find that a low (high) reference level leads to inventory overstocking (understocking), which is illustrated jointly by the loss aversion degree, reference level, and competition intensity. Finally, we conduct numerical experiments to provide engineering confirmations of our theoretical findings and to generate additional insights.