  We apply the recently formulated torque equilibrium spin wave theory (TESWT)
to compute the $1/S$-order interacting $K$ -edge bimagnon resonant inelastic
x-ray scattering (RIXS) spectra of an anisotropic triangular lattice
antiferromagnet with Dzyaloshinskii-Moriya (DM) interaction. We extend the
interacting torque equilibrium formalism, incorporating the effects of DM
interaction, to appropriately account for the zero-point quantum fluctuation
that manifests as the emergence of spin Casimir effect in a noncollinear spin
spiral state. Using inelastic neutron scattering data from Cs$_2$CuCl$_4$ we
fit the 1/S corrected TESWT dispersion to extract exchange and DM interaction
parameters. We use these new fit coefficients alongside other relevant model
parameters to investigate, compare, and contrast the effects of spatial
anisotropy and DM interaction on the RIXS spectra at various points across the
magnetic Brillouin zone. We highlight the key features of the bi- and trimagnon
RIXS spectrum at the two inequivalent rotonlike points, $M(0,2 \pi/\sqrt{3})$
and $M^{\prime}(\pi,\pi/\sqrt{3})$, whose behavior is quite different from an
isotropic triangular lattice system. While the roton RIXS spectrum at the $M$
point undergoes a spectral downshift with increasing anisotropy, the peak at
the $M^\prime$ location loses its spectral strength without any shift. With the
inclusion of DM interaction the spiral phase is more stable and the peak at
both $M$ and $M^\prime$ point exhibits a spectral upshift. Our calculation
offers a practical example of how to calculate interacting RIXS spectra in a
non-collinear quantum magnet using TESWT. Our findings provide an opportunity
to experimentally test the predictions of interacting TESWT formalism using
RIXS, a spectroscopic method currently in vogue.
