I believe the great Eric Dolphy had an answer to this question:
At home (in California), I used to play, and
the birds always used to whistle with me. I would stop what I was
working on and play with the birds… Birds have notes in between our
notes – you try to imitate something they do and, like, maybe it’s
between F and F#, and you’ll have to go up or come down on the
pitch…Indian music has something of the same quality – different
scales and quarter tones.
Here's a nice example of some music that might have started life as a collaboration between Mr. Dolphy and his feathered friends (Although the birds don't get any credits on the label...) :
To add to the fun, we also have the whales and dolphins:
To the point: Since according to Dolpy birds, and also dogs (according to the OP and another answer) and whales seem to learn, improvise and interact musically, they don't make their musical sounds by only by reflex and instinct, and it's not just a form of communication.
Their songs should be considered music by all definitions, unless we arbitrarily decide that only humans can make music.
As for @Shevliaskovic and Stravinsky:
From this I conclude that tonal elements become music only by virtue of their being organized, and that such organization presupposes a conscious human act.
I have to question how Stravinsky could be so certain about what's going on in the brains of certain animals. It sounds like a very limited, antiquated view of things. We know a lot more about animals and how they "think" than when Stravinsky made that statement. For example, it's been proven empirically that dogs engage in some rudimentary forms of thinking and they form true emotional bonds with their owners. If he knew then what we know now, perhaps Stravinsky would have a different opinion about the songs of birds.