Well you do notice in the video that he doesn't say how long it will play before the battery dies (for max playing time, go with D cells instead of AA). However, the speakers in the video look like Tannoy Mercury F1s, which are rated at 87dB sensitivity, which is probably pretty close to the Technics (I couldn't find any info online about those speakers, although
this thread didn't speak highly of them). So yes, I think it will work (I still stand by my estimate of the actual power output, though); I'd just leave the other channel disconnected. Also, I'd probably test it out with a 12V power supply first, before purchasing the cells and holders, using an ammeter. With that, combined with the mAh spec for the battery cells, you should be able to calculate how long the battery will last.
Here's a thread on an electronics forum discussing this exact subject.
I'm still concerned, however, about the lack of cooling for the amplifier IC*, and that's not addressed in the video (even an amp that puts out only a couple of watts would normally have some sort of heat sink).
*ETA: Answered, to some extent: The
manual states that the amp is >= 90% efficient. Presumably (I assumed 90% for calculations) this means that with a power output of 5 watts, the chip would only need to dissipate .56 watts (I do note that a higher power version does include a heat sink and fan). If we further extrapolate, we can calculate the power consumption at 5W output and 12V input (NiMH cells are only 1.2 volts, compared to 1.5 volts for non-rechargeable) to be about 475 mA. With good quality, fully-charged NiMH AA cells, you should be able to get 4-5 hours of playing time.