Along the lines of walking and chewing gum at the same time, this study from the Just lab shows that does indeed take more prefrontal work (directed attention) to listen and watch at the same time. In fact, if you're trying to listen and watch at the same time, you're more likely to lose what you're listening to.
This makes sense with what we see below, and is not surprising that youngsters in general (including young gifted children) struggle with not paying attention to what you said...it may be too much coming in visually to listen.
The main problem we see in our clinic is that unitasking kids are misdiagnosed as having ADD or ADHD ("hyperfocus", e.g. not hearing Mom call when playing a video game or watching TV), or autism. Children who struggle with multi-tasking may indeed have real classroom challenges for certain activities, but weak multi-tasking by itself is not an indicator or disease, and for many, the greatest problems will be had while their brains are still developing.
A final closing thought - It's nice to see studies such as this teasing out the biological process behind challenges with multi-tasking, but wouldn't it be great if as much effort were put into the development of programs that could help kids (and some adults) build up their weak abilities?
Listening and Watching, Multi-tasking fMRI pdf