Given the requirements for millisecond latency, capability to handle burstable read and write workloads, and auto-scaling features, Amazon DynamoDB is the appropriate choice because it is a NoSQL database service that provides fast and predictable performance with seamless scalability. It is designed to handle large-scale, high-velocity data, which is what a mobile gaming application would generate. Unlike Amazon RDS or Amazon Aurora, which are relational databases better suited for structured data and consistent workloads, Amazon DynamoDB can scale automatically to adjust for varying workloads which is typical of mobile gaming applications. DynamoDB also provides built-in support for the handling of large-scale, distributed datasets which suits the expected data size and the requirement for low latency data access.