With the advance of modern technologies, computer-based systems for animals are gaining popularity. In particular, there is an explosion of products and gadgets for pets: wellness monitoring applications (e.g., FitBark and PetPace), automatic food dispensers, cognitive enrichment apps, and many more. Furthermore, the discipline of Animal-Computer Interaction has emerged, focusing on a user-centric development of technologies for animals, making them stakeholders in the development process. Animal-centric technologies have already been developed to support activities of rescue and assistance dogs, to provide environmental and cognitive enrichment for animals in captivity, and to support conservation and animal behavior research. Going beyond human stakeholders poses new exciting challenges for requirement engineering and can be used to significantly expand its boundaries under broader theoretical and methodological frameworks. This paper highlights these challenges and proposes a research agenda for developing methodologies for requirement elicitation and analysis for a user-centric development of computerized systems for non-human users.