What do we know:
1) on "average" based on testing a (fairly common, and random) selection of battery powered devices, Dave showed that most run down to around 1v, before cutting out.
2) for an "average" battery, the 1V point is approximately 80% discharged typically, leaving another 20% of energy unusable.
3) A 100% efficient DC/DC convertor could leverage that extra 20% energy and make it available to the load.
4) No DC/DC convertor is 100% efficient, and their operating efficiency is HIGHLY dependent upon the load placed across them.
5) On average, typical existing DC/DC convertors would be expected to be between 90 & 95% efficient. meaning the extra energy available to an average load can be expected to be between 10 and 15%
Now, you'll note the use of "on average" as this is the important bit! What matters is the average useage of this device not the extreme ends of the normal distribution curve!
It's like claiming your car does INFINITE miles per gallon because you have rolled down a hill with the engine off, and conveniently forgetting to mention how it got to the top of the hill, or that most people don't only drive downhill etc
So if we ignore all the marketing Bull, this product does potentially have some uses. For example, you're giving a presentation and the battery in your wireless mouse goes "flat". You whip out a Batteriser, and you're able to finish your presentation. That's a genuinely usefull scenario.
However, you could also finish that presentation by simply keeping a spare battery in your bag, which would fit any device, and provide 100% more run time, not 10%........
If this device is well designed, cheap, and they actually claim some realistic performance claims (which will be easily testable!) then it has a good future imo, but the blatant marketing spin and frankly, downright lies, published to date do nothing to help their case!