Combine all ingredients; cover and chill.
Make 1/4-inch-deep cuts on both sides of steak, about 1 inch apart in a diamond pattern, with a sharp knife.
Combine steak and teriyaki sauce in a heavy-duty zip-top plastic bag; seal and turn to coat.
Chill 2 hours.
Remove steak from marinade, reserving marinade.
Bring reserved marinade to a boil in a small saucepan.
Grill steak, covered with grill lid, over medium-high heat (350* to 400*F/ 175* to 205*C) 7 minutes on each side or to desired degree of doneness, basting with reserved marinade.
Wrap tortillas in aluminum foil, and place on hot grill 10 minutes or until thoroughly heated.
Cut steak across grain into thin slices, and place evenly down center of tortillas; top with cabbage and Spicy Pineapple Salsa.
Roll up, and serve immediately.