There is another algorithm for computing similarity between time series, which could still be very useful: cross-correlation (also called "coherence" in signals processing). Cross-correlation is O(n log n), so it's perfect for big data applications.
DTW, however, can answer more interesting questions. For example, if you have two performances of a song captured in MIDI, the timing of each note played can vary a little, tempo can fluctuate and sometimes extra notes can also be introduced. DTW can help find the best mapping between two such performances.
It's cool to see it extended to data beyond discrete base/aa values.
The "time warping" aspect also kinda reminds me of the methods used in remote sensing for comparing spectral signatures (SCM/SAM) [ex. 2].
I'd be interested in learning where/how this is being used for problems in finance or economics.
There are a few open-source databases of physiological signals like the ECG used in the video. One is PhysioBank: