People don't always think of Ohm's law.
If you have yellow LED, these LED will drop 2.0 to 2.2 volts.
If you use 2.4 volts supply (2x rechargeable battery), the PIC voltage drop is only 0.2 to 0.4 volts.
The electric Power is calculated from current, and voltage drop!
So the chip remains cool. The value in the datasheet is the current for full voltage drop across the PIC (I think).
This is maybe the reason why the PIC does not burn from LED.
For individual LED resistors should be used if the LED is too bright.
Here is also schematic + source code + datasheets for LED display drive using serial buffers.
I don't think it's the same display as in your photo.
http://pic.hitechworld.org/716pcb/ (directory only not web page)