This question is among the toughest I have read in a long time. Perhaps, a few members can put down their thoughts so that a consensus answer emerges.
There is a part of the listening experience which is hard to pin down in words, but an attempt to do so with the word "musical" can mean a sense of pace and rhythm which synchronizes with the listener inducing a desire for bobbing, weaving, toe tapping or other responsiveness to the experience. An older way of saying this is that "the music is getting to you".
Another way this is evident is when a listener feels the transmitted emotion inherent in musical performances. There might be a smile, relaxation of facial muscles, or its opposite, a look of attentiveness or flow of tears.
Since it is too hard to easily express in words, these examples can at least focus you on the human emotional response to what is being heard. If you fail to experience something akin to these responses then the item you are auditioning is failing to allow this subtle message through. Was it Duke Ellington who stated "it don't mean a thing if it ain't got that swing?" (apology for any misquotation).
Although it is confusing to bring it up, there are performers who lack musicality due to a lack of expressivity in tone, dynamic shading, rhythmic sense. If you think of a dull or uninspired live performance you have endured then you have experienced a lack of musicality, and better equipment can't help that.
Sometimes you can imagine a definition from its opposite.
Whenever one component or another succeeds in being "musical" each successful designer has his/her own way of voicing the product to please the listener.
Designing great equipment is not just a science, but an art.
