As mentioned before the correct terminology for "audiographic" memory is Echoic, however, "audiographic" isn't a bad term. This is because for auditory sensory input to be stored as long-term memories, the information must be visualized.
A simple way to demonstrate is this goes as follows...
Set a reminder for five minutes and make a sound. When the reminder goes off try to recall the sound.
If you are to do this, you'll find that the sound that you recall is almost hollow in a sense. You'll know that you heard the sound, but you won't be recalling the actual sound, you're recalling the idea of it. In other words, your brain, knowing you heard a sound will "jot it down" and later when it's asked what it heard it will "expand" the idea of audio out into your memory of sound.
When it comes to Ted Cruz's case, it still appears he remembering the idea of the sound and the sound itself. I got that from the mention of transcripts. Ted is just remembering the ideas conveyed by the sound of speech with a high degree of accuracy.
The degree of accuracy Ted is able to accomplish while recalling conversations is due to a technique that is well known as "Memory Palaces". This is also known as The Method of Loci (link at the bottom). What is happening is Ted is memorizing the conversations by visualizing the conversation as a transcript and filing it away to be recalled later. I assume that this happens naturally for him, but you can train yourself to be able to do this.