Amazon Kinesis Data Streams is the appropriate service because it caters specifically to real-time data streaming scenarios, allowing the capture, storage, and processing of large streams of data records. Its ability to handle massive simultaneous data streams from numerous sources makes it perfectly suited for monitoring and analyzing IoT device output with minimal latency. This enables businesses to act on insights almost immediately after data generation. The alternatives like database replication or periodic data transfer services do not offer the same real-time processing capabilities and are less suited for scenarios where speed and scalability in data ingestion are critical.