After the world premiere of Amazon’s remake of the 1989 cult classic Road House at SXSW on Friday night, star Jake Gyllenhaal offered a tribute to Patrick Swayze, the performer who originated the lead role of Dalton that Gyllenhaal reprises in the new film. The late Swayze, a Houston native, delivered one of his most soulful performances in an unabashedly pretty silly action movie about a star bouncer who protects a roadside honky-tonk called the Double Deuce from the evil machinations of a corrupt businessman. Swayze, as we all know, had layers. “I’d be remiss if I didn’t [mention] Mr. Swayze,” Gyllenhaal said after the screening, when panel moderator Dax Shepard asked which big-screen tough guy most inspired him as a young man. He grew up…