The Zeeman line components of the magnetic-dipole (M1) 1 s2 2 s2 2p P 1/2 2 - P 3/2 2 transition in boronlike Ar13+ were experimentally resolved by high-precision emission spectroscopy using the Heidelberg electron beam ion trap. We determined the gyromagnetic (g) factors of the ground and first-excited levels to be g1/2 =0.663(7) and g3/2 =1.333(2), respectively. This corresponds to a measurement of the g factor of a relativistic electron in a bound non- S state of a multielectron ion with a 1.5 parts-per-thousand accuracy. The results are compared to theoretical calculations by means of the configuration interaction Dirac-Fock-Sturmian method including electron correlation effects and additional quantum electrodynamic corrections. Our measurements show that the classical Landé g factor formula is sufficiently accurate to the present level of accuracy in few-electron ions of medium nuclear charge number Z.