The physics behind this is simple. When you squeeze the alkaline battery you put mechanical energy into it. Squeezed atoms are forced to be getting nearer to each other. As you squeeze, also the electrons start to spin faster due to decreased radius of their orbits. This requires a lots of mechanical energy, BUT: Now this extra mechanical energy you just put into the electrolyte, can be extracted as electrical energy!(tm)
By this phenomenon new possibilities arise. It is now possible to make high pressure packed batteries. This can be grown into new groundbreaking technology, which can reduce battery size by orders of magnitude for the same capacity, or make the same sized batteries with orders of magnitude more energy!(tm)
Unfortunately there is some drawback. If you increase matter density too much, by squeezing in too much power, you can go beyond the critical mass and the battery can implode ruining all the effort (energy) put into squeezing it.
God thing is, this energy thou adds to the energy of the void, which with current technology we cannot effectively harvest. Maybe in the future it will be possible to recover it. It could then lead to REAL wireless energy transfer of which Tesla and many other people dreamed.
One very good thing about squeezing is The Safety(tm). Properly squeezed batteries cannot make any harm when physically damaged. When battery is damaged and the electrolyte pressure drops rapidly, the temperature will also rapidly decrease. These are known thermodynamics laws. With so much decompression the electrolyte will freeze almost immediately preventing any splashes. The outer foil of the battery can then easily hold frozen electrolyte later, when it heats to ambient temperature, so it will not spill.
This safety feature can have another off-prescription usage: as a drink cooler. You get depleted battery, which still have the very high pressurized electrolyte inside, smash it with something to make is decompress and freeze to nearly zero K temperature, and just drop it inside a glass of a drink, for example beer. With that much difference in temperature, freezing is much faster than using standard, old fashioned water ice cubes.
I think many brilliant uses for this technology is possible.
Cheers!