Wait! We got it all wrong! I think I know how the Batteriser works!
So you know how all these devices can work even when each battery is down to only 1.1 V? Well we are "wasting" all that extra voltage by using brand new 1.5 V batteries in our devices! How much? Well 0.4 V of extra "energy" is in each battery that is not even needed because the device will happily continue functioning even on 1.1 V per cell.
So the Batteriser "throttles down" the voltage on the battery and therefore extends it's life... It lowers the voltage from 1.5 V per cell to what the device needs to just barely stay on (say 1.1 V) and that "extra" 0.4 V that it saves can then be recovered and used later on to drastically extend the life of the battery. Yes! I think that is the magic behind it!
Buck-boost converters work just like that. They can produce constant output voltage even if the battery voltage drops or increases.
Modern electrical devices typically operate as constant power mode, which means in practice that if the battery voltage increases the current consumption will be reduced - and if the battery voltage drops the current consumption increases. Using a buck-boost-gimmick wouldn't produce any real advantage here.
For a device using an electric motor, there will be some advantage though. When the battery voltage increases, the current will increase too. And reducing the battery voltage will reduce the current as well. But reducing the battery voltage will make the motor veryy slooooowwww...
This video "Flash light test with The Batteriser" gives a hint that the output voltage will stay constant as the actual battery gets discharged, so there is boost-regulator inside.
As the actual battery voltage drops the current drawn by the boost-regulator needs to increase in order to keep the output voltage constant. Funny enough, this will discharge the battery a bit faster as the discharge current increases.
Please read Jay_Diddy_B's thorough analysis and excellent simulation on what this means in practice:
https://www.eevblog.com/forum/projects/modeling-an-alkaline-battery-in-ltspice/msg731360/#msg731360As the battery discharge curves show there is very little energy left after the battery voltage has reached the 0.9V cut-off voltage. This means there is hardly any energy left in the actual battery. If there is no energy left, even the Batteriser cannot do any magic tricks here.