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This paper investigates the sum spectral efficiency maximization problem in downlink multiuser multiple-input multiple-output (MIMO) systems with low-resolution quantizers at an access point (AP) and users. In particular, we consider rate-splitting multiple access (RSMA) to enhance spectral efficiency by offering opportunities to boost achievable degrees of freedom. Optimizing RSMA precoders, however, is highly challenging due to the minimum rate constraint when determining the rate of the common stream. The quantization errors coupled with the precoders further make the problem more complicated and difficult to solve. In this paper, we develop a novel RSMA precoding algorithm incorporating quantization errors for maximizing the sum spectral efficiency. To this end, we first obtain an approximate spectral efficiency in a smooth function. Subsequently, we derive the first-order optimality condition in the form of the nonlinear eigenvalue problem (NEP). We propose a computationally efficient algorithm to find the principal eigenvector of the NEP as a sub-optimal solution. Simulation results validate the superior spectral efficiency of the proposed method. The key benefit of using RSMA over spatial division multiple access (SDMA) comes from the ability of the common stream to balance between the channel gain and quantization error in multiuser MIMO systems with different quantization resolutions.