Some have cried violation of counterpoint, but I don't think that is such an issue here. CP is mostly about how notes are linked together on a small scale, and this is rather the network's strong point: it seems to concentrate on the associativity between notes and between chords, and any given moment seems to be composed with a vision that only extends to a few bars (or even just a few beats) around that moment.
The main problem is therefore large-scale structure. For one, recurrence of melodies (at key moments and transpositions) is crucial to creating the emotional value of classical music. None of this appears here.
And secondly, possibly the greatest shortfall of the present neural network (I'm ignoring performance, of course) is the harmonic structure. Classical music, let's say later than medieval and earlier than late-romantic in style, generally has the harmonic structure of a recursive cadence. Harmonic cadences are what give emotional power to harmony, but this NN is painfully incapable of creating any.
That being said, I don't think this problem is inherent to the approach of creating music with NNs. Right now it sounds like what you'd get with a well-crafted Markov chain, but NNs can go beyond this, and this article is exactly the kind of thing that will instigate this evolution.