The development of residential hotels has new practical significance in today’s rural tourism which is heating up and getting more and more attention and development. This paper constructs a service quality evaluation system for residential hotels based on SERVQUAL service quality model and introduces gray correlation analysis and multiple linear regression to analyze the role and influence of residential hotels on rural tourism development. Taking the data of residential hotels in Province S as the research sample, the gray correlation degree and service quality gap of residential hotel service quality were verified, and the interaction between them was verified by regression analysis under different fixed effects. The results show that the gray correlation of safety in the service quality of residential hotels is the highest at 0.7812, the gap of service quality advantage is 0.46 points higher than the mean value of rural tourism tourists’ expectations, and the explanatory degree of the service quality of residential hotels to the development of rural tourism reaches 72.4% in all dimensions. The development of rural tourism can be boosted by improving service quality in residential hotels and meeting the expectations of tourists regarding rural tourism.