This article from Psychology Today is a great discussion of what "play" is. Here's a brief quote from early in the article:
(1) Play is self-chosen and self-directed; (2) Play is activity in which means are more valued than ends; (3) Play has structure, or rules, which are not dictated by physical necessity but emanate from the minds of the players; (4) Play is imaginative, non-literal, mentally removed in some way from “real” or “serious” life; and (5) Play involves an active, alert, but non-stressed frame of mind.
Those points, and others made in the article, read like a good definition of music therapy if you substitute "playing music" for "play".
One reason I choose the name "Kenwood Players" as a performance name for the Friday group is that I wanted to make explicit that "play" aspect of our music making. As I've noted from time to time, it seems to me that our visibly having fun playing engages audiences at least as much as the music itself.
One of the antecedents of "play" is the Old Dutch word "pleien - leap for joy, dance" according to the Oxford American Dictionary.
For me, the most striking correlation between music therapy and play was the author's elaboration of that first point. 1) Play is self-chosen and self-directed - players are always free to quit.
Back when I did music therapy in closed classrooms for emotionally disturbed children, the cardinal rule was it was not mandatory. I always said something like "I'm sure there's other stuff your teacher can find for you to do if you don't want to participate in music." Right off the bat that eliminated the "power struggle" of trying to "make" the children behave. And the corollary to that was that I told them it was my job to find a way for them to participate that they could easily handle.
I never had child choose to not participate, and the teachers were always impressed by the fact I had no real discipline problems.