Whisk shallots, soy sauce, fish sauce, sugar, and Sriracha in a shallow baking dish. Add pork chops and turn to coat. Cover and chill, turning occasionally, at least 1 hour.
Prepare grill for medium-high heat.
Remove pork chops from marinade, scraping off excess, and grill until cooked through, about 3 minutes per side.
Do ahead: Pork chops can be marinated 12 hours ahead. Keep chilled.
Heat 4 tablespoons oil in a small saucepan over medium heat. Add shallots and cook, stirring occasionally, until golden brown and crisp, about 4 minutes. Transfer to paper towels to drain; season with salt.
Whisk vinegar, soy sauce, sugar, and remaining 2 tablespoons oil in a large bowl; season with salt and pepper. Add purslane, watermelon, and Pickled Watermelon Rind; season with salt and pepper and toss gently to coat.
Serve pork chops with watermelon salad topped with fried shallots.