Preheat a grill to medium high. Brush a baking sheet with olive oil. Place the pizza dough on the pan and turn to coat with the oil; set aside to bring to room temperature.
Slice the pork lengthwise down the center almost all the way through, then open like a book and flatten with your hands. Season the pork with salt and pepper and brush all over with 2 tablespoons teriyaki glaze. Brush the pineapple and onion slices with olive oil and season lightly with salt and pepper.
Brush the grill grates with olive oil. Arrange the pineapple and onion on one side of the grill and the pork on the other side. Grill the pineapple and onion until tender and lightly charred, 2 to 3 minutes per side; transfer to a plate. Grill the pork until cooked through, about 6 minutes per side; transfer to a cutting board.
Stretch the pizza dough into a 9-by-12-inch rectangle on the baking sheet. Reduce the grill heat to low; place the dough directly on the grill and cook until puffed on top and charred on the bottom, 1 to 2 minutes. Flip and top with the cheese. Cover and cook until the crust is cooked through and the cheese is melted, 2 to 3 minutes. Transfer to a cutting board. Cut the pineapple and pork into bite-size pieces; scatter over the crust along with the onion. Drizzle with the remaining teriyaki glaze and sprinkle with the cilantro. Cut into pieces.