Rate-splitting multiple access (RSMA) is a novel multiple access technique that breaks messages into common and private parts to mitigate interference in a flexible manner. Motivated by its robustness, RSMA is promising in multibeam satellite systems, where a satellite broadly serves terrestrial users through a multibeam multicast transmission with a full frequency reuse among all spot beams. In the multibeam satellite system, there are heterogeneous traffic demands among the spot beams. To meet the different traffic requirements for the spot beams, we present a novel RSMA-enabled rate-matching framework that matches the traffic demand for each spot beam through partially decoding inter-beam interference. We optimize the precoding and power allocation of the private/common messages to achieve the minimization of the difference between data rates and traffic demands among all spot beams. Numerical results show that the proposed framework significantly outperforms conventional transmission schemes in terms of meeting the traffic demands for the spot beams.