A U.S. Marine sniper seeks out Viet Cong with a high-powered rifle and scope near Que Son, Vietnam, Dec. 13, 1965. (AP Photo)
That rifle looks to be a Winchester Model 70. I seem to recall that's what the Marines were using at the time. During Desert Storm, my snipers used a mix of Winchester 70s and Remington 700s. But, our rifles had been worked by the Marksmanship Unit at Benning and were very, very nice.
Sniping, like nearly every facet of military life has changed drastically since then.