I'm mostly curious because I used the HTK for my thesis and would like to know how they compare (besides, one being just 'newer').
The main difference here is hooking DNN output to an HMM decoder, replacing GMMs, and possibly even more important the training process they use to get the DNN fairly efficiently. That's the biggest thing -- GMMs, at least the last time I've looked, can be trained and adapted much quicker than a DNN.
I think the HTK doesn't use neural networks at all. What it does is simply computes the MFCC of the sound signal and use it as input to a chain of HMM models. Well, "simply" that, plus the dozens of refinements and tweakings to make that work well.
Here, I guess they do some sort of preprocessing on the sounds features using their deep neural networks before feeding the whole thing to the HMMs.