LEDs, Voltage and Resistors
These lights (and many other cheap/disposable LED devices) count on the internal resistance of the batteries to prevent enough current to damage them from flowing. Each LED can use 10-20mA each at 3V, and putting them in parallel allows them to share the total current available.

This can be demonstrated by putting NiCd batteries in place of the current batteries; NiCd batteries have a much lower internal resistance than alkaline or ZnC batteries, so the LEDs will either get much brighter or blow out completely (provided they can supply enough voltage (2.4V) to light them, of course).

And since they're in parallel, you cannot run them directly from an Arduino even with a resistor. You will need to use a high-side or low-side switch to power them directly from the power supply.