The rapid urbanization process has brought many pollution NIMBY facilities, and the associated pollution NIMBY conflicts have become one of the important factors restricting social stability. With the advent of the media era, new media has become the main channel for the public to recognize risks and master information, which greatly aggravates the social amplification effect of NIMBY conflict risk. In this case, it is of great significance to explore the interest relationship among the local government, the new media, and the local people and their roles in the NIMBY conflict. Based on the stakeholder theory, this paper constructs a three-party evolutionary game model of the local government, the new media, and the local people and carries out numerical simulation on the evolutionary model using MATLAB. The results show that the local government adopts a certain degree of regulatory strategy for the new media, the new media adopts the strategy of publicizing facts, and the local people adopts the strategy of nonresistance, which are the stable strategy points of the evolutionary game among the three stakeholders in the NIMBY conflict. The local government’s intervention in rumors to a certain extent is conducive to promoting the new media to publicize facts of the pollution NIMBY facilities and to restrain the local people’s choice of resistance strategies. The local government’s punishment to the new media spreading rumors should be kept above a certain level to restrain the new media spreading rumors. When the local people’s resistance reaches a certain level, the local government’s intervention will break down and the new media will become hyperactive. The results of this paper can provide some enlightenment for the stakeholders in pollution NIMBY conflicts and deepen the understanding of multiple interest conflicts and their resolution. Finally, this study proposes to build information sharing mechanism, information communication mechanism, trust mechanism, network governance mechanism, and public participation mechanism, so as to resolve the construction risk of pollution NIMBY facilities and improve the overall social welfare level.