The distributed telescope array offers promise for conducting large-sky-area, high-frequency time-domain surveys. Multiple telescopes can be deployed at each observation site, so intrasite observation task scheduling is crucial for enhancing observation efficiency and quality. Efficient use of observable time and rapid response to special situations are critical to maximize scientific discovery in time-domain surveys. Besides, the competing scientific priorities, time-varying observation conditions, and capabilities of observation equipment, lead to a vast search space of the scheduling. So with the increasing number of telescopes and observation fields, balancing computational time with solution quality in observation scheduling poses a significant challenge. Informed by the seminal contributions of earlier studies on a multilevel scheduling model and global scheduler for a time-domain telescope array, this study is devoted to further exploring the site scheduler. Formulating the observation scheduling of multiple telescopes at the site as a cooperative decision-making problem, this paper proposes GRRIS, a real-time intrasite observation scheduling scheme for the telescope array using graph and reinforcement learning (RL). It employs a graph neural network to learn node features that can embed the spatial structure of the observation scheduling. An algorithm based on multi-agent RL is designed to efficiently learn the optimum allocation policy of telescope agents to field nodes. Through numerical simulations with real-world scenarios, GRRIS can achieve up to a 22% solution improvement over the most competitive scheme. It offers better scalability and subsecond decision speed, meeting the needs of observation scheduling control for future distributed telescope arrays.