The local nature of resonant inelastic x-ray scattering (RIXS) spectroscopy permits the use of single-site or cluster-based theories to simulate experimental spectra. These theories focus on the central atom (mostly the transition metal) and treat the correlations with surrounding ligands or adjacent transition metal complex through some hybridization parameters determined by fitting with the experimental spectra. Simulated spectra are mostly compared with experimental ones where the probed elements are the dominant species. It is still interesting to examine how far one can extend this kind of local treatment to the case of a dilute dopant system where the dopants themselves are the primary focus. We consider the experimental RIXS spectrum of a 10% Mn-doped Sr₃Ru₂O₇ compound at the Mn L₃ edge resonance. Using a single-ion based RIXS theory for Mn³⁺ (the dopant oxidation state) in conjunction with the experimental data, we unravel the microscopic interaction parameters (crystal field energies, superexchange couplings) of the Mn³⁺ ion in the host material. Based on our theoretical modeling and fit, we estimate the energy scale of the non-spin-flip and spin-flip dd excitation along with identifying the charge transfer excitation energy boundary.