How do MS-TDNNs work?
So I think you understood that a MS-TDNN has two parts: a conventional TDNN that calculates state probabilities for each frame and kind of a perceptron on top of it linking the states of several frames to a word. The later part is doing the segmentation. Its connections aren't trained, but just used for running BP and train the TDNN.

The segmentation is obtained by some other algorithm (I don't remember exactly, but something like dynamic time warping). In normal DNN-HMM hybrid systems the DNNs are trained separately to predict the correct state for each frame. The error function is calculated on frame level!

This is not optimal as we do not care so much about each state being correct, but the final text. WER is calculated on world level. MS-TDNNs try to solve this by having this extra layer that allows passing a word level based error to BP. This is very similar to todays methods called sequence training.

Neither TDNN nor MS-TDNN are recurrent networks.

If you are interested in RNNs and ASR systems that do not require HMMs I would recommend you to look at CTC objective that does indeed learn the alignment automatically.