I think that different music can be appreciated in different ways. Some music is most definitely artistic. You don't have to sit down and listen to it, and it's not a crime to listen to it while working or doing something else, but if you do take the time to sit in a comfortable position, close your eyes and contemplate nothing but your audio stimuli, then it will be time very well spent. A few examples of music that I think fits into this category:
Each of these is arguably a complex masterpiece deserving of your full attention at least once in your life.
Conversely, there are also valid pieces of music that are designed to be a part of the room rather than compete for your full attention. They used to be called furniture music but are now more commonly known as ambient music. They are perfect for adding mood to a scene rather than trying to take center stage. Such music includes:
While you may or may not glean anything from sitting down and listening to such music, it can really add to the atmosphere of a bath or massage, for instance.
These are just two extremes of music, and of course you can listen to either type of music while doing something else or while giving it your full, undivided attention. My point is that different music is designed to be listened to in different ways. There's no right or wrong way to listen to a piece of music, and especially to listen to music in general.