Looking at a Strokesaver book of Muirfield published in 2002, it clearly shows two tees for Hole #15. the one on the right was used for the 2002 Open Championship. The tee on the left, forcing play directly over the three cross bunkers, is marked as the "Medal Tee." Carrying a ball over those bunkers from the Medal Tee requires a drive of only 200 yards.
From the Championship Tee, the hole played at 415 yards. From the Medal Tee, the hole plays at 394 yards.
The view in the video clearly shows them playing the hole from the Medal Tee in 1966.