To speak about "what is art" without considering intent is to miss the crux. However, sometimes the chaotic can be "a great work of art" in the colloquial sense, but not technically unless an artist changes or contextualises it. Also consider how engaging with non-art effectively turns it into art in a subjective sense, eg. scenery. Practically, it simply depends on where, or if, people want to draw that line. For some, every element of life is art and for others, none.
I say, look at this conversation that the work is not simply about, but IS. The work is this conversation.
This conversation could be turned into a work of art with some imaginative alterations or contextualising, but in itself it's not art unless you are one to view life through a romantic imaginative lens.
I think intent is important only to the extent that it illuminates the object as art. It could be the artist's "intent" is not as insightful as the critic, that is, the critic may identify aesthetic possibilities never conceived by the artist. The right of wrong of it then rests with appreciation and analysis, the kind of which takes the work up as art, of course (rather than, per above, epistemology and so forth).
But as you say, contextualizing it is important; more than this: contextualizing separates art from non art, if it is understood that there is such thing as a context of art appreciation. I think form and aesthetic rapture are what define the context of art.
What an interesting thing to say, but right on the money: if I take a conversation, of any kind whatever, and consider it AS art, then the context turns away from analysis (though analysis discloses aesthetics, as in, look at that bird's plumage, the way it reflects the light, isn't it beautiful?) toward something else. The question is, what is this? If it is just a conversation, I would think of it as part of a stage production with dramatic impact? Or perhaps the form, the analogue as opposed to digital nature of the spoken word, the rise and fall of intonation or emphasis, and so on.
Meredith Monk! Now she makes conversation into art. Literally!