Mitch, I pulled up a copy of the WG AGO 53-55 on line for my review. Line 31 states; “Military Qualifications and Date (i.e., infantry, aviation and marksmanship badges, etc.)"
The combination of the previous posts is your answer. The “SS Rifle” designation is not the type of rifle he carried or qualified with. It is the designation of the level of Marksmanship Badge; Sharpshooter, Marksmanship Badge.