The Rivet Gun is used to shoot Rivet Blades and lop off limbs (the advertised "strategic dismemberment" aspect of the game). You aim it "perpendicular to the limb you are trying to cut off," which translates to twisting the Wiimote around to line up the shot. At least we now know the game isn't entirely point and click!
[Screen via Nintendo Power table of contents (pdf link)]