Context. CO gas has been detected in ~20 debris discs, typically classified as CO-poor or CO-rich. We present observations of the CO-rich HD 121617 debris disc as part of the ALMA survey to Resolve exoKuiper belt Substructures (ARKS). Aims. We model local CO line profiles in the HD 121617 debris disc to investigate optical depth, CO mass, and temperature. HD 121617 is a well-suited ARKS target due to its previously detected CO emission and moderate inclination, reducing the effect of Keplerian shear. Methods. Using high-resolution ALMA Band 7 observations of 12CO J=3─2 (26 m s−1, 0⋅'' 1), we create local line profiles by aligning and stacking spectra in concentric annuli of 0⋅'' 02 width. These profiles are modelled with both a toy model and a RADMC-3D model that includes projection effects and Keplerian shear. Results. The resulting local profiles are Gaussian-shaped and broad due to the effect of Keplerian shear. Fitting a RADMC-3D model to the 13CO data, we find that an optically thick model (temperature of 38 K and mass of 2 × 10−3 M⊕) reproduces the data, particularly the enhanced intensity at orbital azimuths of ~±45° and ±135°, which forms an X-shape in the velocity integrated intensity map, as well as the broader 12CO linewidth compared to 13CO. Scaling this model by the ISM abundance ratio (~77) also reproduces the 12CO data, but high optical depths and model assumptions limit mass constraints. Conclusions. Keplerian shear causes azimuthally averaged line profiles to appear Gaussian regardless of optical depth; therefore, we caution against using the local line profiles to distinguish between optically thin and thick emission. We constrain the mean molecular weight to 12.6−1.1+1.3, dependent on model assumptions. Although model dependent, our 13CO results indicate that C18O might also be optically thick in CO-rich debris discs, contrary to previous assumptions, and that the mean molecular weight is significantly higher than if H2 were the dominant gas species, suggesting a non-primordial composition.