I'm like this, but when I have too much caffeine I notice that it's harder to turn the monologue off. It becomes a little shouty in fact. Brains are weird.
I play time-attack puzzle games; and some of my best times have been while I'm listening to an audiobook, music or deep in thought about some emotional problem. It feels like I actually perform both tasks better if I'm doing them simultaneously because my "vague processing" isn't interrupted by my "sharp processing" and vice versa.
I have this problem with music/sound specifically. I cannot remember it at all. For example, I have favourite artist that I heard all of his albums 50+ times. If you play a random track of his to me I won't be able to identify it. Another example; My favourite all time soundtrack that I heard countless times, I cannot recall how it goes. If somebody asks me to "sing" the melody I will fail miserably. Oh and I don't know lyrics of any song. Any. I tried to learn though...
I still get tired of listening to the same tracks over and over again :( .