Basically you're implying binary neurons, neuroevolution (which works on non-differentiable functions) etc. aren't a thing. Or at least they're not (working with) neural nets.
It's almost like SGD just made decades of AI research into neural networks just vanish.
Nobody is claiming that the definition of "differentiable programming" should be identical to the definition of "neural net". The claim is, if you want to assign a name to the thing that TensorFlow, PyTorch, and similar frameworks do, it's "differentiable programming".
If you want to make a non-differentiable neural net, knock yourself out. The research still exists and nobody is stopping you.
But while we're talking about terminology, I'd encourage you to stop referring to the units as "neurons". The false analogy to biology just confuses people.
It's almost like SGD just made decades of AI research into neural networks just vanish.