We report the first empirical demonstration that resonant inelastic x-ray scattering (RIXS) is sensitive to collective magnetic excitations in S=1 systems by probing the Ni L3 edge of La2-xSrxNiO4 (x=0, 0.33, 0.45). The magnetic excitation peak is asymmetric, indicating the presence of single and multi-spin-flip excitations. As the hole doping level is increased, the zone boundary magnon energy is suppressed at a much larger rate than that in hole doped cuprates. Based on the analysis of the orbital and charge excitations observed by RIXS, we argue that this difference is related to the orbital character of the doped holes in these two families. This work establishes RIXS as a probe of fundamental magnetic interactions in nickelates opening the way towards studies of heterostructures and ultrafast pump-probe experiments.