Heat oil in a nonstick skillet over medium-high heat. Add shrimp; sauté 5 minutes. Remove from skillet; set aside.
Combine pineapple and next 5 ingredients (pineapple through lime juice) in skillet. Combine vinegar and cornstarch, stirring until well-blended; add to skillet. Bring to a boil, and cook 1 minute or until thickened, stirring constantly.
Return shrimp to skillet. Reduce heat to low, and cook 1 minute or until thoroughly heated, stirring constantly. Remove from heat; stir in cilantro. Serve over rice.