Update: The Android version of Shazam has now received this update as well. Here's the new changelog posted to the Play Store.
This release brings full track playback in Shazam, powered by Rdio. Once you’re connected, you can play any track and carry on listening to the music as you discover more in the app. Shazam a song to get started.
Shazam, the company whose app uses a phone or tablet's microphone to identify a song or TV show, has partnered with Rdio to offer users full in-app song playback.