What is the advantage of using RNN with fixed timestep length over Neural Network?
It's true that they both use 3 samples to predict the next sample. But the difference is obviously how they learn it. Deep Neural Nets will treat time-distributed samples such as they were single sample at once. However, RNN will learn it as a sequence by its sequential nature, part by part. 

Each activation layer of (uni-directional) RNN will take a part of a sequence, make prediction and feed the prediction on that part forward to the next activation layer which will take the next part of the sequence as input. Important part is that the prediction is feeded forward so that the next neuron learning the next part of the sequence will also affected from the prediction of the previous neuron as well as the input sequence, unlike classical neural networks. It can get easy to understand when you look at the visual example below:



Hope I could help.