The multi-energy conversion system (MCS) plays an important role in improving the utilization of energy resources and realizing the energy transition. With the application of the new generation of information technologies, the new MCS can realize real-time information interaction, multi-energy collaboration, and real-time demand response, in which energy suppliers can intelligently motivate consumers' energy use behavior. In this paper, an MCS coupled with a cloud platform is proposed to address information explosion and data security issues. Due to the development of Internet technology, the increasing energy data, and the serious energy coupling, it is difficult for traditional optimization methods to deal with the interaction between participants of the MCS. Therefore, the non-cooperative game is used to formulate the interactions between participants with the aim of maximizing the energy suppliers' profit and minimizing the customers' cost. It is proved that the game model is an ordinary game with one Nash equilibrium. The simulation was performed with a gradient projection algorithm and the results show that the proposed MCS improves energy utilization efficiency through energy conversion while ensuring consumer satisfaction, and benefits both the customers and suppliers by reducing the energy consumption cost and the peak load demand, which effectively improve the supply quality and enrich the energy consumption patterns.