Emergent Language (EL) focuses on the emergence of communication among artificial agents. Although symbolic communication channels more closely mirror the discrete nature of human language, learning such protocols remains fundamentally difficult due to the non-differentiability of symbol sampling. Existing approaches typically rely on high-variance gradient estimators such as REINFORCE or on continuous relaxations such as Gumbel-Softmax, both of which suffer from limitations in training stability and scalability. Motivated by cognitive theories that emphasize intrapersonal processes preceding communication, we explore self-play as a substrate for language emergence prior to mutual interaction. We introduce Vector Quantized Emergent Language (VQEL), a novel architecture that incorporates vector quantization into the message generation process. VQEL enables agents to perform self-play using discrete internal representations derived from a learned codebook while preserving end-to-end differentiability. Moreover, the resulting vector-quantized codebook naturally induces a symbolic vocabulary that can be directly transferred and aligned during subsequent mutual play with other agents. Empirical results show that agents pretrained via VQEL self-play achieve more consistent symbol alignment and higher task success when later engaged in mutual interaction. These findings position self-play as a principled and effective mechanism for learning discrete communication protocols, addressing key optimization and representational challenges in emergent language systems.