Catalysis of the addition of a second methyl group to methylated peptidyl-arginine. Methylation is on the same terminal nitrogen (omega nitrogen) residue that was previously methylated, resulting in asymmetrical peptidyl-N(omega),N(omega)-dimethylated arginine residues.
S-adenosyl-L-methionine:-L-arginine N-methyltransferase (-Nomega,Nomega-dimethyl-L-arginine-forming)