Is deep learning a Markov chain in disguise?

Andrej Karpathy's post "The Unreasonable Effectiveness of Recurrent Neural Networks" made splashes last year. The basic premise is that you can create a recurrent neural network to learn language features character-by-character. But is the resultant model any different from a Markov chain built for the same purpose? I implemented a character-by-character Markov chain in R to find out. First, let's play a variation of the Imitation Game with generated text from Karpathy's tinyshakespeare dataset.