LED lights on 1.2 V battery
LED's have a forward voltage, this can be tweaked by the manufacturer for different purposes, generally below 1 V for visible light is hard, but possible to buy (likely infrared or red with a phosphor to bring it up to visible)

The battery has a certain amount of internal resistance, being rechargeable generally means it is lower than non rechargeable batteries, it is likely each LED can handle enough current without damage to essentially have the battery's internal resistance act as a current limiting resistor

This is assuming that green circuit board out of frame on your picture doesn't have some small LED constant current driver.