Interestingly, the neural net used is not really that deep: it has only two hidden layers (see figure 3 in the paper[1]). The innovations are really in how the researcher is representing inputs using different "modalities" (see section 4.1 "Feature Representation"), generating a training corpus (section 4.3), and training the neural net (sections 4.4 and 4.5).
[1] http://arxiv.org/pdf/1509.01549v2.pdf