Nope, not Yosemite. The opening scene is at the Matterhorn, on the Swiss side of the mountain. It looks like the flyer started from either near or just above an alpine refuge hut on the original route on a ridge called (I think I remember this correctly) the Hornli ridge. Even after 35 years absence, it looked the same to me.

Then, there is a short cut near Rio De Janeiro, Brazil.

The rest of the video is somewhere in the European alps. Obvious, because of the beautiful green mountain-sides.