Combine ground round and water in a 4-quart pressure cooker; stir with a fork until thoroughly blended. Stir in tomato paste and next 12 ingredients.
Cover cooker with lid, and seal securely; place pressure control over vent and tube. Cook over high heat until pressure control rocks back and forth quickly. Reduce heat until pressure control rocks occasionally; cook 15 minutes.
Remove from heat; run cold water over cooker to reduce pressure. Carefully remove lid.
Remove and discard bay leaves, stirring well. Serve chili over hot spaghetti, and top with cheese and onion. Serve with oyster crackers.