I believe that dataflow/reactive programming is the answer and the direction to follow as its principles are pretty close to how neurons work; plus it can be made to work on top of von neuman architectures.
I bet there is more, just buried under varied publications, and I am sure that they created a DSL for their specialized brain based chip.
The most obvious and battle tested way to program a NeuroSynaptic hardware is to create models of the brain (any application) in an algorithm and burning it with an HDL into an fpga or an fpaa. For computation of numerical entities, a small controller running a customized embedded software is used.
At the very least, if they have a cortex in software, it would create a ethical (?) way to experiment with the logic by enabling/disabling pieces and seeing what happens.
Sounds a bit like cargo-cult to me. We already tried to spawn amoebas from electro-charged soup of chemicals and it didn't work.
The brain's "programming language" refers more the to the idea of what makes the brain's biological structure work to produce human perception.
Even then, there is a neuroscience branch called neural coding that apparently acknowledges the existence of a neural code; but judging from the wikipedia entry their approach seems still too "low level".