S.P.E.C.I.A.L. intro videos
You're right: There is a video for every SPECIAL stat. They are "triggered" simply by booting the game; after the Bethesda logo you will probably get shown one of them at random. However, this doesn't mean you have to keep booting the game to watch them all - just head over here.
Watch all seven S.P.E.C.I.A.L. videos on the official Bethesda YouTube channel