What is meant by this theory that there are only 3 possible kinds of cognitive loads? I don't understand this theory that states there are only three kinds of mental loads:


  The theory is that there are basically three different kinds of
  demands or loads that you can make on a person: Cognitive (thinking
  and remembering), Visual, and Motor.


Source, Posted on February 17, 2011 by Susan Weinschenk.

What about things like listening to someone speak? Or if someone's learning to play a musical instrument and is trying to hit the right note. Is this only in the context of interaction design.
The source you mention is a web blog about computer and office work. The blog doesn't describe a 'theory', not even a hypothesis for that matter, it just outlines a starting point for a popular scientific blog on cognitive load in everyday life. It all depends on the task what adds mental load. Every input, let it be acoustic (e.g. speech), visual (e.g. computer tasks), touch or internal mental processes can all increase cognitive load. 

I can recommend reading the wiki page on cognitive load as a starting point to better understand different aspects of cognitive load theory.