Its not clear from the description, but I suspect the logarithmic tone curve is probably applied by hardware, to the output coming directly from the sensor. In other words, this is on chip correction of the raw analog values probably in the amplification stage before the signal hits the A/D converter.
In which case it would not be possible to emulate in software.
The correction may however be applied after the A/D stage (which I doubt), in which case it might be possible to process the raw output from the camera in a similar manner.
If it were possible to do this in software, you would require a camera capable of outputting raw video frames, and already able to produce extremely good low light performance.
Even the best canon P&S sensors really don't fall in to this category, the sensors are too small, and the noise levels are not comparable to this Sony, so the technique, if it could be applied, would still not produce results as impressive as the video, but it might provide some improvement over the standard off the shelf results.
I suspect you may need to look for patents relating to the subject to figure out when and how this is done.
It is pretty impressive however. Thanks for sharing.