For the marinade: In a small bowl, mix the spices, salt, pepper, lime juice, and oil to make a paste. Place the steak in a shallow dish and rub the paste evenly over both sides. Cover and let marinate for 1 to 4 hours.
For the salsa: Light a charcoal grill about 30 minutes before you're ready to cook or preheat a gas grill to medium-high.
Slice off the leafy top of the pineapple and just enough of the bottom so the fruit rests flat on a cutting board. Slice off the skin with a sharp knife, cutting from top to bottom and taking off as little of the flesh as possible, rotating the pineapple as you go. Discard the skin. Cut out any "eyes" with a paring knife and discard. Slice the fruit away from the core in 4 or 5 slabs.
Place the pineapple slabs on the hot grill and grill until the fruit is just beginning to show some browning, 1 to 2 minutes per side, 4 to 5 minutes per side if you want it charred.
Let the pineapple cool for a few minutes, then dice. In a medium bowl, mix the diced pineapple, onion, cilantro, lime juice, vinegar, olive oil, salt, and chile and blend well.
To cook the steak: Grill the steak for 5 to 6 minutes on each side, or slightly longer for well-done meat. Remove from the grill and let rest for 10 minutes before slicing.
Meanwhile, place the tortillas on the hot grill and grill for 10 seconds on each side, then wrap in a cloth napkin to keep them warm.
Slice the steak across the grain into 1/2-inch-thick slices and arrange on a serving platter. Place the tortillas and the bowl of salsa on the table and serve family-style.