Powered by large language models, the conversational capabilities of AI have seen significant improvements. In this context, a series of role-playing AI chatbots have emerged, exhibiting a strong tendency toward anthropomorphism, such as conversing like humans, possessing personalities, and fulfilling social and companionship functions. Informed by media dependency theory in communication studies, this work hypothesizes that a higher level of anthropomorphism of the role-playing chatbots will increase users' media dependency (i.e., people will depend on media that meets their needs and goals). Specifically, we conducted a user study on a Chinese role-playing chatbot platform, Xuanhe AI, selecting four representative chatbots as research targets. We invited 149 users to interact with these chatbots over a period. A questionnaire survey revealed a significant positive correlation between the degree of anthropomorphism in role-playing chatbots and users' media dependency, with user satisfaction mediating this relationship. Next, based on the quantitative results, we conducted semi-structured interviews with ten users to further understand the factors that deterred them from depending on anthropomorphic chatbots. In conclusion, this work has provided empirical insights for the design of role-playing AI chatbots and deepened the understanding of how users engage with conversational AI over a longer period.