They claim to be using a LSTM, and I believe that any RNN-like architecture should (in theory) be able to learn a loop pedal.
If you aren't familiar with RNNs, think about it like a NN that instead of learning a input -> output function, learns a (input, state) -> (output, newState) function
If you aren't familiar with RNNs, think about it like a NN that instead of learning a input -> output function, learns a (input, state) -> (output, newState) function