Yup, must be something similar to a Joule thief intended to drive an LED from a single 1.5V cell, the kind you find in cheap solar garden lights. Basically a voltage booster and regulator circuit to keep the output voltage more or less constant even when the cell voltage drops with use.
Unfortunately, there are a few problems with this premise. First, the voltage booster ramps up the voltage by producing short, relatively high voltage pulses. This is acceptable for powering a simple LED or the like but does not work with more complex circuits. Adding a good regulator circuit will (ideally) keep the output voltage constant without the unwanted ripples. But in practice, it seldom works really well.
Then there is another technical problem with the voltage booster concept. Even if it does provide a constant 1.5V output until the actual cell voltage drops below any useful level (say, 0.5 or even 0.3V) the battery will not be able to provide much current due to the limitations and relatively inefficient nature of voltage booster circuits. So it may work for low-power devices but that's about it.
Maybe the Batteriser is somehow more efficient in some aspects but at the end of the day, the energy capacity of any battery cell is finite. You may boost the output voltage with an electronic circuit, but only at a modest current (maybe tens of miliamps at most from an AA cell). Not even taking into account the extra size of the Batteriser clip, which I suspect wouldn't fit in many electronic devices.