A search for Weakly Interacting Massive Particles (WIMPs) was conducted with the single-phase liquid-xenon detector XMASS through inelastic scattering in which $^{129}$Xe nuclei were excited, using an exposure ($rm 327; kg times 800.0 ; days$) 48 times larger than that of our previous study. The inelastic excitation sensitivity was improved by detailed evaluation of background, event classification based on scintillation timing that distinguished $gamma$-rays and $beta$-rays, and simultaneous fitting of the energy spectra of $gamma$-like and $beta$-like samples. No evidence of a WIMP signal was found. Thus, we set the upper limits of the inelastic channel cross section at 90% confidence level, for example, $4.1times 10^{-39} ;{rm cm^2}$ for a $200; {rm GeV}/c^2$ WIMP. This result provides the most stringent limits on the SD WIMP-neutron interaction and is better by a factor of 7.7 at $200;{rm GeV}/c^2$ than the existing experimental limit.
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