I'm not an expert on machine learning or DSP, but I do know just enough of each to suspect this isn't anywhere near as impressive as it seems. A distortion pedal is essentially just a waveshaper [1]. Think of audio in digital terms as just a series of numbers. A waveshaper is just a simple mathematical function. To apply it, you literally just apply the function to each value in the input stream and there's your outp…
This would be true for a linear impulse response, however for this kind of effects you need both state/memory (like a convolution) and non-linearity (like a waveshaper), which is why people use RNN's and CNN's