not quite sure about the difference between RNN and feed forward neural net
The authors state that's the formulation for a feed forward deep learner, so you're exactly right. The two equations at the bottom of the page are where they formulate their recurrent neural net

The response is 

$\hat{Y} = \text{softmax}(W^2Z_t+b^2) $ 

and the hidden state is 

$Z_{t-j} = \text{tanh}(W^1[Z_{t-j-1},X_{t-j}] + b^1), j \in\{k,...,0\}$

The authors punt to this paper for implementation details, but the recurrent nature here comes from directly articulating your hidden state off of your most recent hidden state $Z_{t-j-1}$ (which involves the input $X_{t-j-1}$ from the last time step).

Hope this helps!